Aging rate of dielectric permittivity and loss for PMN ­ PT based single crystals manufactured by continuous-feeding Bridgman with alternating current poling

Aging rate (AR) of dielectric permittivity ( ¾ 33T / ¾ 0 ) of ternary Pb(In 1 / 2 Nb 1 / 2 )O 3 ­ Pb(Mg 1 / 3 Nb 2 / 3 )O 3 ­ x PbTiO 3 (PIN ­ PMN ­ x PT, x = 26 and 30 mol % ) and binary Pb(Mg 1 / 3 Nb 2 / 3 )O 3 ­ x PbTiO 3 (PMN ­ x PT, x = 30 mol % ) single crystals (SCs) grown by the continuous-feeding Bridgman method (CF-BM) were investigated. The AR of dielectric permittivity was 0.6 ­ 2.0 %/ decade, whereas that of dielectric loss of the SCs was 1 ­ 8 %/ decade. Even though the SC growth methods were di ﬀ erent, the AR of CF-BM PMN ­ 30PT SCs were similar with that of conventional one-charge Bridgman method (OC-BM) SCs. In this work, the AR of the SCs possessing high ¾ 33T / ¾ 0 more than 8000 by alternating current poling (ACP) was 4 to 7 times larger than that of PZT ceramics. It is noted that SCs with higher ¾ 33T / ¾ 0 tend to exhibit higher AR. Given that the SCs were in an unstable state within 10 h after poling, the AR presented in this paper was calculated from 10 to 100 h after poling. We hope this work provides a new insight for evaluating the properties of the SCs and addresses the fact that SCs for piezoelectric devices should be properly selected by considering whether their AR could let them work normally during their entire lifetime.


Introduction
Ferroelectric relaxor-PbTiO 3 single crystals (SCs) such as binary Pb(Mg 1/3 Nb 2/3 )O 3 xPbTiO 3 (PMNxPT) and ternary Pb(In 1/2 Nb 1/2 )O 3 Pb(Mg 1/3 Nb 2/3 )O 3 xPbTiO 3 (PINPMNxPT) have attracted considerable interest over the past decades owing to their outstanding piezoelectric and electromechanical properties. 1)7) These unprecedented electromechanical responses are only observed in the vicinity of, so-called, morphotropic phase boundary, and electric field driven phase transformations between ferroelectric symmetries were attributed to underlying mechanisms. 8) Nevertheless, their strain mechanisms still deserve more investigations due to the absence of direct evidence associated with field-induced phase transformtaions. 9) Meanwhile, ternary PINPMNxPT SCs have been developed to improve their stabilities against external stimulus with sufficiently high piezoelectric coefficient (d 33 ) of 15002500 pC/N when their PT content (x) is ranged from 28 to 32 mol %. 10) Given that their superior piezoelectricity and electromechanical coupling to ceramic counterparts are key for practical applications, relaxor-based SCs have been continuously fabricated into electromechanical devices 11) 13) including ultrasonic (US) transducers 14)17) and piezoelectric transformers. 18) Furthermore, advancements in relaxor-based SCs have accelerated the developments of high frequency transducers, leading to high resolution and depth imaging. 19) Thus, relaxor-based SCs have been considered as one of promising candidates for next-generation US transducers fabricated into medical probes. 20) Generally, the conventional growth method for relaxor-PT SCs is an one-charge Bridgman method (OC-BM), by which crystals larger than 100 mm in diameter and length can be produced. 21)23) However, compositional inhomogeneity coming from the segregation of elements in use leads to non-uniformity in TiO 2 contents along the growth direction, resulting in inconsistencies in dielectric and piezoelectric properties within SC ingots and each wafer. 21), 22) To mitigate the composition-related issues, a new growth technique, continuous-feeding Bridgman method (CF-BM), was suggested and well succeeded in controlling the compositional uniformity. As a result, large-sized PMN PT SC ingots (80 mm in diameter, 320 mm in length, and 13 kg of weight) were commercially manufactured since 2011. 24)26) For ferroelectric-based piezoelectric materials to be macroscopically piezoelectric, poling is an indispensable process to align randomly-distributed domains and thus obtain high piezoelectric and dielectric properties. A direct current poling (DCP) has been widely used for such domain-texturing processes. However, since the first demonstrations of a dynamic alternating current poling (ACP) by Yamamoto and Yamashita et al., it has been of considerable importance due to its further enhancements in dielectric and piezoelectric properties. 27),28) So far, more than 20 papers relevant to ACP have been reported in the past few years. 29)48) Aging is namely a time-dependent spontaneous variation under the absence of external stress and electric field. It is generally accepted that thermodynamic equilibrium states associated with defects are responsible for the aging, and linear correlations with the log time scale are commonly believed in aging behaviors. 49) For medical US probes or other applications, the fast aging of given materials is a critical obstacle and thus deteriorates the qualities of images with their shorter lifetimes. Though the aging rate (AR) of ferroelectric ceramics have been already studied by many researchers, 50)53) there are few studies on the AR of dielectric permittivity (¾ 33 T /¾ 0 ) and loss of relaxor-based SCs. It is worthy noted that Chang et al. reported the AR of OC-BM PMN30PT SC by DCP and ACP were 1.25 and 1.95 %/decade, respectively. 31) However, the AR of loss in PMN30PT SCs was not primarily investigated and discussed in the aforementioned literature. Therefore, the purpose of the current work is to systematically study the AR of compositionally dissimilar (PIN)PMNPT SCs manufactured by the state of art CF-BM SC growth methods. Under different poling conditions including ACP and DCP, comparative experiments were conducted to study how dielectric properties are varied in comparison with commercialized PZT ceramics (¾ 33 T / ¾ 0 > 5000). Figure 1 shows the schematic illustrations of (a) the OC-BM in which compositional segregations naturally occur during crystal growth and (b) the CF-BM wherein raw materials are continuously added into a Pt crucible during crystal growth to ensure consistency in properties. The variations of TiO 2 contents within the ingot of the OC-BM and CF-BM were reported as «4 and «0.5 mol %, respectively. 26) [001]-oriented PMN30PT, PINPMN30PT and PIN PMN26PT wafers from [011] grown ingots (JFE Mineral Co., Japan) were prepared by the CF-BM method. Furthermore, in order to compare aging properties between high performance PZT ceramics and SCs above, two kinds of PZT ceramics, i.e., PZT 5H and PZT K5500 (Tayca Co., Japan), were also prepared as comparisons. Since AC voltages in terms of its involved energy vary with respect to the shape of waveforms, we adopted root mean square (rms) voltages for all ACP conditions in order to compare with DC voltages. The term 'rms voltage' also known as the effective or heating rate of alternating current is associated with the generation of identical heat at the same time in a resistor. Therefore, the AC voltages can be properly compared with the DC voltages. The SCs were ACP using bipolar sine waves in the air from temperature of 40 to 80°C with electric fields of 3 9 kV rms/cm, 0.150 Hz and 12100 cycles. To compare with the ACP effect of the SCs, we also performed DCP in the air from temperatures of 4080°C with electric fields of 38 kV/cm for 60300 s. In addition, PZT 5H and PZT K5500 plates were DCP in silicone oil with 20 kV/cm at 80°C for 600 s. The specific poling conditions for the samples are shown in Table 1.

Experiment
Their dielectric capacitance and loss were measured 0.1 h after poling at 2327°C. The free ¾ 33 T /¾ 0 and clamped dielectric permittivity (¾ 33 S /¾ 0 ) were calculated from the capacitances measured by an impedance analyzer (HP 4194 A, USA) at 1 kHz and at the two times of anti-resonant frequency (2 f a ), respectively. Calculated bar mode electromechanical coupling factors (k 33 ) were obtained from ¾ 33 T /¾ 0 and ¾ 33 S /¾ 0 according to the following Eq. (1). 34) Calculated As relaxor-PT SCs are very sensitive to external temperatures, we modified ¾ 33 T /¾ 0 values that were not measured at 25.0°C according to the Electronic Industries Alliance (EIA) 198-1 standard 54) by the following formula (2): MC 25 is a material property at 25.0°C, MC T is a material property at a measured temperature, and T is a measured temperature according to the EIA standard. TDC is a temperature dependence coefficient and relaxor-PT SCs have usually large TDC reported by Luo et al. 38) and Sun et al. 39) AR of ¾ 33 T /¾ 0 and dielectric loss for samples were calculated by the following formula (3).  T /¾ 0 and loss for the SCs at 1 kHz were obtained by a computer-controlled LCR meter (Hioki IM-3570, Japan) at every 0.1°C in a temperature range of 30250°C.
We conducted structural analyses after poling by X-ray diffraction (XRD) (Rigaku Corp., RINT 2200 model, Japan) with Cu K¡ 1 monochromatic radiation. The (004) peaks of CF-BM PINPMN30PT poled by ACP and DCP after 1 and 1700 h were measured at the room temperature.

Result and discussion
The poling conditions and the electrical properties of the SCs and PZT ceramics in the current experiments are listed in Table 1.
The AR(¾ 33 T /¾ 0 ) and AR(loss) of the CF-BM PIN PMN30PT poled by ACP and DCP with the 8 kV rms/cm are shown in Fig. 3(a). The ¾ 33 T /¾ 0 of PINPMN30PT after DCP and ACP 100 h was about 5140 and 8980, respectively. In addition, the AR(¾ 33 T /¾ 0 ) of the ACP PINPMN30PT from 10 to 1000 h was 1.7 %/decade which was 3 times that of the DCP PINPMN30PT. The AR(loss) of PINPMN30PT poled by ACP was 5 times that of DCP.
When the AC electric field was applied to PINPMN 30PT SCs, the internal polarization reversal occurred several times, resulting in the crystals were fully poled. However, there is no polarization reversal during the DCP process. This may be the reason why ACP for 2 s had better poling effects than DCP for 5 min. Figure 3(b) shows how ¾ 33 T /¾ 0 changes in the period from 1 to 1000 years for the CF-BM PINPMN30PT poled by ACP and DCP and high performance PZT ceramics K5500 with respect to calculated AR(¾ 33 T /¾ 0 ). It was found that although the ACP PINPMN30PT SCs possess high AR(¾ 33 T /¾ 0 ) than that of DCP SC, the absolute value of the decrease in ¾ 33 T /¾ 0 is acceptable within the lifetime of US application no more than 10 years. Although some materials may possess high AR(¾ 33 T /¾ 0 ) after poling, the absolute value of ¾ 33 T /¾ 0 varied with time is very small in their lifetime, which is not obvious impact in actual applications. We carefully argue that the poling voltage is a key factor affecting the performance of the samples. As the coercive field (E c ) of PINPMN26PT is 5.6 kV/cm, 26) the voltages of 3 and 8 kV rms/cm used for the poling are approximately equal to 0.5 and 1.4 times the E c , respectively. Normally, a voltage 3 times E c is used for poling. Therefore, the samples performed by ACP and DCP were not sufficiently poled, and the dielectric properties of PIN PMN26PT SCs treated by 8 kV rms/cm were better than those treated by 3 kV rms/cm.
The AR properties of PZT 5H ceramics are shown in Fig. 5(a), and both AR(¾ 33 T /¾ 0 ) and AR(loss) are the lowest in this work (0.3 and 3 %/decade, respectively). Figure 5(b) shows the temperature dependence of dielectric permittivity and loss (TDDP&L) of PZT 5H. Its Curie temperature (T c ) decreased by about 4°C after DCP compared with the unpoled PZT 5H samples.
In order to show the AR properties of all samples in the current experiments, the relationships between AR(¾ 33 T / ¾ 0 ) and ¾ 33 T /¾ 0 (100 h) and between AR(loss) and dielectric loss (100 h) are shown in Fig. 6. It is worthy noted that the AR(¾ 33 T /¾ 0 ) of all samples varies from 0.32.0 %/ decade, and the SCs possessing higher ¾ 33 T /¾ 0 tend to show faster AR(¾ 33 T /¾ 0 ). The PZT K5500 has almost the same ¾ 33 T /¾ 0 as DCP CF-BM PMN30PT over 5800, and it has lower AR(¾ 33 T /¾ 0 ). We consider that how to decrease the AR of high-performance SCs is our future works.
The AR(loss) of all samples varied from 18 %/decade. In addition, the AR(loss) of most samples was higher than their AR(¾ 33 T /¾ 0 ), which is consistent with the conclusions of most cases, i.e., the rate of dielectric loss is higher than that of capacitance. 49) In Figs. 4(a) and 4(b), due to the different poling methods, the variational trends of dielectric loss in short time (0.11 h) and medium time (1 10 h) were different. As even some samples exhibit drastic changes, thus we showed all AR(loss) were in the range of the long time (10100 h).
The cause of aging is generally believed to be that after the poling electric field be removed, the domain gradually returns to the orientation before poling treatment to elimi-nate internal stress reported by Schulze and Ogino. 49) The internal bias field could promote domain recovery, 55) so the larger the internal bias field is, the more serious the aging is. And the mechanical quality factor (Q m ) of PZT ceramics increase with the increase of internal bias field   reported by Book "Ferroelectric Physics" edited by W.-L. Zhong. 56) By investigating the Q m of all samples in this work, for same composition, the sample with larger Q m tends to show higher AR, which is consistent with the above description about aging of PZT ceramics K5500.
In order to figure out how phase transition temperatures (Trt) of the samples are changed after different poling conditions and whether ACP has a positive effect on samples, we measured TDDP&L for all SC samples. The TDDP&L of PINPMN30PT SC poled by ACP and DCP is shown in Fig. 7.
The Trt of CF-BM PINPMN30PT was 102°C before poling 26) and it increased by 5.5°C after ACP while it decreased by 0.7°C after DCP. The Trt shift after the ACP of the CF-BM 24PIN46PMN30PT SC in this study and the OC-BM 25PIN43PMN32PT SC reported by Ma were similar. 40) As shown in Fig. 8, the Trt of PINPMN26PT after DCP greatly increased by 7°C. However, by using 3 kV rms/cm voltage, the ACP samples showed that Trt decreased by 2.7°C and by using 8 kV rms/cm voltage ACP sample showed Trt decreased by 4.1°C compared with the unpoled samples Trt of which was 138°C. 26) This result indicated that the Trt shift are different between high Trt > 130°C and low Trt < 110°C ternary PIN-PMN xPT SCs.
According to Fig. 9, Trt of the CF-BM PMN30PT decreased from 92 26) to 88.3°C after ACP and to 80.3°C after DCP.
As we can see in Figs. 79, the dielectric properties of SCs in the room temperature are correlated with the position of phase change temperature Trt. Therefore, the temperature dependence of dielectric permittivity of each SC is very important to indicate these AR and phase change phenomena.
We suspected that AR was caused by the change of lattice constant of the SCs after poling time. Therefore, the XRD of (004) surface of the PINPMN30PT after poling 1 and 1700 h was investigated.
In Fig. 10, the DC poled PINPMN30PT showed lower peak intensity with lower angle (99.13°), and by ACP method, peak of (004) of PINPMN30PT moved to higher angle (99.30°), considering that it is caused by the decrease of c-axis in lattice constant. Besides, the higher dielectric properties are responsible for the higher peak intensity and angle shift, which is consistent with conclusion of Luo et al. 38), 45) However, there are no big differences of XRD between 1 and 1700 h, showing that the AR is not caused by a large lattice constant change after poling.

Conclusion
In summary, the aging properties (dielectric permittivity and loss) of [001]-oriented PINPMNPT and PMNPT SCs manufactured by CF-BM with respect to different poling conditions and compositions were investigated for    the first time. It should be noted that relaxor-SCs possessing higher ¾ 33 T /¾ 0 tend to show higher AR, while PZT ceramics showed low AR, which indicates that PZT ceramics have excellent time stability. We speculated the reason why the ARs of various SC samples were different is due to different propensity in domain recovery after poling. Given that internal bias field E i can promote domain recovery, the higher the E i , the faster the AR. In addition, E i and mechanical quality factor Q m are positively correlated in PZT systems. Therefore, we investigated the Q m of all samples and found that the SCs with large Q m tend to show large AR(¾ 33 T /¾ 0 ). These AR of the CF-BM PMN 30PT SCs were similar with that of conventional OC-BM SCs even though the SC growth method is different. To our best knowledge, the aging of dielectric loss, at present, has not been systemically studied, and we claim that more investigations are still needed. For the SCs, their dielectric losses were quite low (0.20.4 %), but their AR were very high (18 %/decade). Meanwhile, the dielectric loss of PZT ceramics were much higher (1.31.8 %) than that of the SCs. However, their AR were at low level (3 %/ decade) and proved good stabilities in this experiment. Although the AR(¾ 33 T /¾ 0 ) of some SCs were higher than those high performance PZT, the absolute value of ¾ 33 T /¾ 0 decrease is acceptable in the lifetime of practical applications. This experiment may provide a new insight to evaluate the performance of the SCs. As future studies, we will focus on how to reduce the AR of high ¾ 33 T /¾ 0 SC, which stabilizes and prolongs the lifetime of devices. We hope the current work may have a positive impact on ultrasound applications.