Stress-induced phase transition in lead-free relaxor ferroelectric composites

Accepted Manuscript Stress-induced phase transition in lead-free relaxor ferroelectric composites Lukas M. Riemer, K.V. Lalitha, Xijie Jiang, Na Liu, Christian Dietz, Robert W. Stark, Pedro B. Groszewicz, Gerd Buntkowsky, Jun Chen, Shan-Tao Zhang, Jürgen Rödel, Jurij Koruza PII:

S1359-6454(17)30557-8

DOI:

10.1016/j.actamat.2017.07.008

Reference:

AM 13905

To appear in:

Acta Materialia

Received Date: 20 March 2017 Revised Date:

30 June 2017

Accepted Date: 4 July 2017

Please cite this article as: L.M. Riemer, K.V. Lalitha, X. Jiang, N. Liu, C. Dietz, R.W. Stark, P.B. Groszewicz, G. Buntkowsky, J. Chen, S.-T. Zhang, Jü. Rödel, J. Koruza, Stress-induced phase transition in lead-free relaxor ferroelectric composites, Acta Materialia (2017), doi: 10.1016/ j.actamat.2017.07.008. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Stress-Induced Phase Transition in Lead-Free Relaxor Ferroelectric Composites

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Lukas M. Riemera, Lalitha K.V. a, Xijie Jianga, Na Liua, Christian Dietza, Robert W. Starka, Pedro B. Groszewiczb, Gerd Buntkowskyb, Jun Chenc, Shan-Tao Zhangd, Jürgen Rödela & Jurij Koruza,a,* a

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Department of Materials and Geoscience, Technische Universität Darmstadt, 64287 Darmstadt, Germany (L.R.: [email protected], L.K.V.: [email protected], X.J.: [email protected], N.L.: [email protected], C.D.: [email protected], R.W.S.: [email protected], J.R.: [email protected]). b Institute of Physical Chemistry, Technische Universität Darmstadt, 64287 Darmstadt, Germany (P.B.G.: [email protected]; G.B.: [email protected]). c Department of Physical Chemistry, University of Science and Technology Beijing, Beijing 100083, China (J.C.: [email protected] ). d National Laboratory of Solid State Microstructures and Department of Materials Science and Engineering, College of Engineering and Applied Science, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China (S.-T.Z.: [email protected])

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* Corresponding Author. E-mail address: [email protected], Tel: +49 6151 162 1686, Postal address: Alarich-Weiss-Straße 2, 64287 Darmstadt, Germany.

Keywords: ferroelectric; piezoelectricity; composites; phase transition; lead-free.

Piezoelectric materials are considered an enabling technology generating an annual

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turnover of about 20 billion $. At present, lead-based materials dominate the market with

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the known risk to health and environment. One of the three key competitors for their replacement is the class of sodium bismuth titanate (NBT)-based relaxor ferroelectrics, the use of which is limited by thermal depolarization. An increased thermal stability has recently been experimentally demonstrated for composites from Na1/2Bi1/2TiO3-6BaTiO3 with ZnO (NBT-6BT:xZnO). However, the exact mechanism for this enhancement still remains to be clarified. In this study, piezoresponse force microscopy and

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Na NMR

spectroscopy were used to demonstrate that the incorporation of ZnO leads to a 1

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stabilization of the induced ferroelectric state at room temperature. Temperature-dependent measurements of the relative dielectric permittivity ε´(T), the piezoelectric coefficient d33 and the strain response revealed an increase of the working temperature by 37 °C. A simple

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mechanics model suggests that thermal deviatoric stresses stabilize the ferroelectric phase and increase as well as broaden the temperature range of depolarization. Our results reveal a generally-applicable mechanism of enhancing phase stability in relaxor ferroelectric

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materials, which is also valid for phase diagrams of other ceramic matrix composites.

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1. Introduction

Ferroelectric materials are essential for piezoelectric applications and modern electronic components. The dominating materials, first and foremost compositions based on Pb(Zr,Ti)O3 (PZT), all contain lead [1]. Unfortunately, lead is hazardous and prolonged

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efforts have been made to advance lead-free alternatives [2]. Among the promising candidates to partially replace PZT are the Na1/2Bi1/2TiO3 (NBT) -based* solid solutions [2], for example with BaTiO3 (BT) [3]. This system reveals a morphotropic phase boundary

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properties [4-6].

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(MPB) at a BT content of 6-7 mol.%, wherein the material possesses relaxor ferroelectric

In the proximity of the MPB, the average structure obtained by X-ray and neutron scattering techniques commonly presents a pseudocubic symmetry [7-9]. However, a phase mixture of rhombohedral and tetragonal symmetry on a local scale was observed by using transmission electron microscopy (TEM) [9,10]. A locally non-cubic structure of NBT-xBT

*

The authors would like to point out that according to IUPAC recommendations, with electronegativity taken as the ordering principle, the preferable nomenclature is Na½Bi½TiO3-6BaTiO3 (NBT) and not Bi½ Na½TiO3-6BaTiO3 (BNT) as is often used in literature for historical reasons.

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was further evidenced by recent investigations employing nuclear magnetic resonance spectroscopy

of

sodium

(23Na

0.94(Na1/2Bi1/2)TiO3-0.06BaTiO3

NMR)

[5,11].

(NBT-6BT),

an

For

the

irreversible

MPB

composition

electric-field-induced

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transition from a non-polar (non-ergodic relaxor) to a long-range ordered ferroelectric state with macroscopic remanent polarization was observed [12,13] and an electric fieldtemperature phase diagram was reported [14]. Analogous to the electric-field-induced

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temperature phase diagram was constructed [15].

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phase transitions, stress-induced transitions were also detected and a corresponding stress-

A major challenge for the technological use of NBT-based systems is a pronounced reduction of macroscopic piezoelectric properties at the depolarization temperature, which for the NBT-6BT composition occurs at about 100 °C [2,16]. Various techniques have been discussed to assess the depolarization temperature [17]. The depolarization is initiated

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through a randomization of domain structure as evidenced by piezoelectric and ferroelectric measurements at the depolarization temperature Td and is finalized by a ferroelectric to

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relaxor transition at TF-R [18].

Td can be increased by applying an external electric field during heating [19]. An increase

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in Td of NBT-BT by chemical modifications is not expected without considerably decreasing the piezoelectric properties. Moreover, a natural mutual interdependence between good piezoelectric properties and enhanced thermal stability was established for a variety of ferroelectric solid solutions and doped systems [2,20,21]. At the same time the anisotropic flattening of the Gibbs free energy near a phase transition promotes a high piezoelectric response but reduces the stability of domain orientation causing premature depolarization [21,22]. A solution for this quandary was recently demonstrated by the 3

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development of a (3-0)-type composites without thermal depolarization up to 130 °C [23]. These composites consisted of the relaxor ferroelectric NBT-6BT and the semiconductor ZnO. Isothermal bipolar hysteresis loops, temperature-dependent measurements of the

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relative dielectric permittivity ε´(T), and retained d33 measurements were used to quantify the depolarization behavior. A charge order model was proposed, that explains the enhanced thermal stability with a partial compensation of the depolarization fields at pores

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and interfaces through the free electrons of ZnO.

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In this study, unpoled NBT-6BT:xZnO composites were investigated by means of polarization and strain analysis, piezoresponse force microscopy (PFM), Kelvin probe force microscopy (KPFM) and 23Na NMR at room temperature. A single particle model is used to estimate the thermal stress in the composites in order to assess its influence on the relaxor to ferroelectric transformation. Furthermore, temperature-dependent in situ d33,

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dielectric permittivity, and large-signal strain measurements were used to gain further insight into the thermal depolarization behavior.

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2. Experimental Section

Sample preparation: 0.94(Na1/2Bi1/2)TiO3-0.06BaTiO3 powder was prepared by means of

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the conventional solid-state synthesis method. Stoichiometric amounts of powders of Bi2O3 (99.975 %), BaCO3 (99.8 %), Na2CO3 (99.5 %), and TiO2 (99.6 %) (all Alfa Aesar), were weighed and milled for 24 h in ethanol at 250 rpm in a planetary ball mill (Fritsch Pulverisette 5). The dried powders were calcined in closed alumina crucibles at 900 °C for 3 h with a heating rate of 5 K min-1. The obtained NBT-6BT powder was ground by mortar and pestle, milled for 24 h in ethanol at 250 rpm, and subsequently dried. The powder was

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sieved with a 160 µm nylon sieve and annealed in closed alumina crucibles at 1100 °C for 3 h in order to coarsen the particles.

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The annealed NBT-6BT powder was ground by mortar and pestle, sieved (160 µm sieve) and weighed together with ZnO nano-sized powder (25 nm, 99.5 %, PlasmaChem GmbH, Berlin) to form mixtures with ZnO/NBT-6BT mole ratios of x = 0.1, 0.2, 0.3, and 0.4. A

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final milling step of 24 h in ethanol at 250 rpm was used to obtain the final powder mixture. For analytical purposes, disks with a diameter of 10 mm were manually cold-pressed, cold

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isostatically compacted at 40 MPa and sintered in closed alumina crucibles at 1012 °C for 1 h with a heating rate of 9 K min-1. As a reference, 10 mm NBT-6BT disks from noncoarsened powder were sintered in closed alumina crucibles at 1150 °C for 3 h with a heating rate of 5 K min-1. To avoid volatilization of bismuth and sodium during sintering all

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samples were embedded in atmospheric powders with the same composition. Methods: The microstructure was characterized by scanning electron microscopy (SEM) (Philips XL30 FEG) and density measurements (Archimedes method). XRD measurements

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were performed on ground and annealed samples with a Bruker D8 diffractometer in Bragg-Brentano geometry and locked couple mode using Cu Kα radiation. For electrical

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measurements the samples were ground to a thickness of 0.6 mm and coated with a layer of silver paste. The burn-in of the electrodes and the annealing of the samples were performed simultaneously at 550 °C for 30 min with a heating rate of 5 K min-1 and slow cooling. Samples were poled at room temperature for 20 min at 6 kV min-1, 24 h before measurement.

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Polarization and strain as a function of electric field were measured with a triangular field up to 6 kV mm-1 at 1 Hz using a Sawyer-Tower circuit equipped with an optical sensor. The same electric field was also used to investigate the temperature-range between 25 and 140

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°C with a TF Analyzer 2000 (Aixacct).

PFM and KPFM measurements for the characterization of the local domain morphology and surface potential, respectively, were performed using a MFP-3D atomic force

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microscope (Asylum Research, Santa Barbara). The measurements were acquired using

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electrically conductive cantilevers of the type ASYELEC-01 and AC240TM, (Asylum Research, Santa Barbara) with nominal free resonance frequencies of 70 kHz and 60 kHz, respectively, and nominal force constants of 2 N m-1. Images were taken at a scan rate of 0.5 Hz with a resolution of 256 × 256 pixels. For the overview PFM measurements, an ac driving voltage of 3 V (peak amplitude), and a drive frequency close to the tip-sample

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contact resonance frequency which was approximately 300 kHz in the single frequency PFM mode were used. For the high-resolution PFM images, we used the dual ac resonance tracking mode [24] applying two drive frequencies f1 and f2 close to the contact resonance

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frequency (frequency difference ∆f = f1 − f2 = 8 kHz, drive voltages for both signals 5 V).

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KPFM [25] was performed in standard lift mode using a lift height of 50 nm. The sample was polished as described in ref. [26]. Temperature and frequency-dependent permittivity measurements were performed with a Hewlett Packard 4192 LF Impedance Analyzer from room temperature to 450 °C and a heating rate of 2 K min-1. In situ d33 values as a function of temperature were measured by the converse method with a Polytec VDD-E-600 Vibrometer Front-End and a Polytec

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OFV-505 Sensor Head using an amplitude of 20 Vpp, a frequency of 1 kHz, and a heating rate of 2 K min-1. Na magic angle spinning (MAS) NMR spectra were recorded with a Bruker AVANCE III

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600 MHz spectrometer operated at a frequency of 158.745787 MHz. A 4 mm MAS probe was employed for spinning prism-shaped (1 mm thick) ceramic samples at 10 kHz. A single-pulse experiment with a pulse length of 0.75 µs, a recycle delay of 1.0 s and a dwell

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time of 0.2 µs ensured appropriate excitation and recording of the spectra. The spectrum of

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NBT-15BT was used as a reference for the intensity ratio between the satellite and central transitions (ST/CT ratio), in order to account for non-ideal probe response. The cubic content in composite samples was determined from the spectra as reported previously [10].

3. Results and Discussion

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3.1. Room Temperature Structure and Properties 3.1.1. X-Ray Diffraction and Microstructure

The results of the phase analysis of samples with different mole ratios (x) of ZnO over

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NBT-6BT, ranging from 0.0 to 0.4, are compared in Figure 1a and 1b. The relative intensities and the peak positions of the constituents and additional phases are provided in

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the lower part of the figure [7,27]. As expected, with increasing x, the intensities of the ZnO peaks increased. A peak of nearly constant intensity at approximately 35.2° in ZnO containing samples (Figure 1b) cannot be assigned to any of the nominal constituents. Based on the literature describing the phase evolution of bismuth and titanium containing ZnO varistors, a TiZn2O4 spinel phase may have formed - albeit a single peak is not sufficient to identify a phase [28]. Back-scattered electron (BSE) images of sintered,

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ground, and polished samples are displayed in Figure 1c and 1d. Two distinct solid phases can be identified: dark isolated grains and a bright continuous matrix.

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XRD data and BSE images confirm that the samples mainly consist of NBT-6BT and ZnO. According to the concept of connectivity, the microstructures may be classified as (3-0)type composites [29]. The microstructural characteristics of all investigated compositions are summarized in Table S1. The grains of the ZnO phase feature planar surfaces and have

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a grain size independent of composition, while the grain size of the NBT-6BT matrix

3.1.2. Ferroelectric Properties

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decreases with increasing ZnO content.

Figure 2 a-d shows the first and the third cycle of the bipolar strain and polarization

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hysteresis loops of unpoled samples at room temperature. The electric field with positive polarity induced a large strain and polarization response in the virgin samples at about 3 kV mm-1 (Figure 2a, c), which is attributed to a field-induced phase transition from the non-

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ergodic relaxor to the ferroelectric state and by domain switching [30,31]. For NBT-6BT this transition occurs at the lowest field and is confined to a narrow range of the electric

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field. After field removal, a remanent strain (Srem) and polarization (Prem) were obtained owing to the irreversible nature of the phase transition and the domain switching process [9,31]. The largest strain and polarization values were obtained for NBT-6BT without any introduction of ZnO (x = 0.0). The maximum and remanent strains and polarization gradually decreased with increasing ZnO content. The bipolar strain and polarization hysteresis of the third cycle are depicted in Figure 2b and 2d, respectively. Note that the strain loops are vertically shifted for a better 8

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comparison. The maximum strain suffers only a small decrease, while a larger decrease was observed for the negative strain and thus the total strain decreased with increasing ZnO content. The switchable polarization (2Prem) of the composites presents only minor changes

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compared to the first cycle, while the polarization was noticeably reduced for NBT-6BT as compared to the first cycle. The coercive field determined for the third cycle as the mean of the intercepts with the x-axis is presented in Figure 2e. The maximum value of

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approximately 3.7 kV mm-1 was obtained for x = 0.1. With an increasing amount of ZnO, a continuous decrease of Ec was observed. Figure 2f presents characteristic strain values

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measured during the first cycle. A general trend of decreasing strain response with increasing x is obvious. This effect can be attributed to the strain incompatibility between the elastically-hard inclusions and the matrix [32].

The strain hysteresis loop of unpoled (virgin) NBT-6BT results from three main effects: the

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inverse piezoelectric effect, domain switching, and phase transformation strains [31]. The reduction in remanent polarization from the first to the third cycle in NBT-6BT is predominantly caused by the absence of phase transformation strains. As this reduction

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hardly occurs for the composites, we suggest that there is less phase transformation during

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poling for the composites. This indicates that the amount of the non-ergodic relaxor phase in virgin samples (before the application of the electric field) is reduced upon the incorporation of ZnO.

2.1.3. Piezoresponse Force Microscopy & Nuclear Magnetic Resonance Measurements

The surface topography, PFM amplitude, and phase images of polished and annealed NBT6BT and NBT-6BT:0.1ZnO samples are presented in Figure 3. The amplitude response of 9

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the PFM signal is related to the local magnitude of the piezoelectric coefficient, while the phase shift with respect to the excitation is a measure of the out-of-plane polarization direction. On the one hand, a weak phase contrast and an absence of any domain-related

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features for both signals are discerned in NBT-6BT (Figure 3a-c), as reported previously [26]. On the other hand, the PFM amplitude and phase images of NBT-6BT:0.1ZnO exhibit a clear contrast. ZnO grains were identified through a surface contact potential difference

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(CPD) between the ZnO grain and the NBT-6BT matrix as measured with a Kelvin probe force microscope (VCPD ≈ 207 mV, see inset in Figure 3g). In Figure 3d-f an overview

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image is given, while Figure 3g-i presents a single ZnO grain in another sample of the same type. In both cases, a lamella-like domain structure with distinct contrast was observed, which cannot be seen in the topography images. These results suggest a locally-induced ferroelectric state in the adjacent NBT-6BT matrix, which was facilitated by the ZnO

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inclusion.

It should be noted that the surface state of a ferroelectric system can be altered by free charges [33] or modified stress fields [34]. Therefore, NMR spectroscopy was used to

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probe the bulk of the samples. NBT-6BT based materials exhibit a complex local structure

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that depends on the actual electric state of the sample. While NBT-6BT samples in the relaxor state contain a considerable amount of the cubic phase, ferroelectric samples (i.e., poled NBT-6BT) present a non-cubic symmetry in the entire local structure [10]. The amount of the cubic phase in NBT-based ceramics can be determined by using 23Na solidstate NMR spectroscopy and analyzing the ST/CT ratio [10]. A ratio of 1.5 is expected if the cubic phase is absent in the sample, whereas a smaller ST/CT ratio indicates the presence of a cubic phase.

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Figure 4a displays the

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Na MAS NMR spectra of two unpoled NBT-6BT samples with

different mole ratios of ZnO: 0.0 and 0.1. Both spectra present a narrow intense component in the middle (central transition - CT) and a broad envelope of spinning sidebands (satellite

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transitions - ST). The relative intensity of the spinning sidebands envelope is larger for samples with ZnO than for the control sample of pure NBT-6BT. This fact evidences a decrease of the cubic phase content when a composite with ZnO is formed, indicating the

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formation of a ferroelectric phase. The cubic phase content can be quantified based on the ST/CT ratio. Figure 4b displays the amount of cubic phase and the ST/CT ratio for both

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samples displayed in Figure 4a, taking into account a calibration procedure with non-cubic, ferroelectric NBT-15BT. A cubic phase content of 23 % was found in pure NBT-6BT, an amount that was also observed in a previous investigation [10]. For the composite sample, the cubic content decreased to 11 %. The influence of ZnO addition on the local symmetry

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and reduction of the cubic phase of the NBT-6BT phase indicates that a substantial volume of the NBT-6BT matrix is in a ferroelectric state in the composite, a result that corroborates the observations made with PFM.

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3.1.4. Stress-Modulated Relaxor-to-Ferroelectric Transition

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Bipolar strain hysteresis loops, PFM, and NMR data evidence the presence of an induced long-range ordered ferroelectric state in virgin composite materials, prior to the application of an external electric field. Recently it was shown that a transition into the long-range ordered ferroelectric state can be achieved by applying electric [12,13] or mechanical uniaxial stress fields [15]. Considering the difference in the coefficients of thermal expansion (CTE) between ZnO and NBT-6BT (αNBT-6BT ≅ αNBT ≅ 7·10-6 K-1 [35], αZnO ≅ 4.3·10-6 K-1 [36]), residual thermal stresses are expected in the composites. Thus, the long11

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range ordered ferroelectric state may be favored due to thermal stress in NBT-6BT:xZnO composites.

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In a first approximation, the composite can be considered as a dilute solution without superposition of stress fields. Thus, the model of a single particle in an infinite isotropic matrix can be used to determine the resulting stress field [37]: ∆∆ , 1 +  1 − 2  + 2E E

 =

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a   = − ∙   , 

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 =

1 a   ∙   . 2 

(1)

(2)

(3)

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Here σR is the stress at the particle matrix interface, ∆α = αM - αP is the difference in CTE between the matrix and the particle, and ∆T is the cooling range. νM,P and EM,P are the Poisson's ratio and Young's modulus of the matrix and particle, respectively. σr and σt

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denote the radial and tangential stress components, a the particle radius, and r the distance of a point to the center of the particle. Equations 1 to 3 describe a stress field with strong

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deviatoric character and zero hydrostatic component. The cooling range was estimated to ∆T = 978 K, while other parameters were taken from the literature: ENBT-6BT = 100 GPa [38]. EZnO = C11 ≅ C33 ≅ 210 GPa [39], and νNBT-6BT = νZnO ≅ 0.3. With these values the σR at 25 °C amounts to -388 MPa. The resulting stress field is schematically depicted in Figure 5a.

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To compare this multiaxial stress state with the stress-temperature phase diagram obtained from uniaxial experiments [15], the shear-dilatant transformation criterion is chosen to calculate the critical transformation stress σk [40]. For the inclusion model the shear-dilatant

1  − 2 2 + 2 − 3 2 + 3 − 1 2 = 2! . 6 1

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transformation criterion is equivalent to the von Mises criterion [41]:

(4)

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To determine the critical transformation stress σk of NBT-6BT, the uniaxial critical relaxorto-ferroelectric transition stress σRe-Fe of ref. [15] is applied. For σ1= σRe-Fe, σ2=0 and σ3=0

"# =

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Equation (4) results in 1 #  . 3 $%&$

(5)

The critical transformation stress σ∗( for the multiaxial stress state in terms of σRe-Fe is

σ∗( =

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obtained by combining Equations 4 and 5 and applying σ1= σr, σ2,3=-1/2 σr: 2  . 3 $%&$

(6)

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For a σRe-Fe of approximately -325 MPa at 25 °C, σ∗( equals to -217 MPa. With this threshold value and Equation 2, the critical radius of transformation rk can be calculated. To

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estimate the volume fraction of transformed material ϕT, a cubic coordination of ZnO particles is chosen and the composite is described as a single ZnO sphere within a cube of the NBT-6BT matrix. A two-dimensional projection of this model is presented in Figure 5b, where b is the distance between the body and the face center of the cube. To evaluate the interactions of stress fields in the composite specimen, the stress at the face center σb is calculated using the particle size for the ZnO from Table S1. The resulting values are presented in Table 1. 13

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The calculated volume fraction of the transformed material is smaller than that one measured with NMR spectroscopy. This discrepancy can be explained with a nucleation

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and growth process. In ferroelectric/relaxor composites with a core-shell structure, the ferroelectric core of same material and grain reduces the driving force required for the relaxor-to-ferroelectric transition because it serves as a nucleus [42]. In the present case,

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the stress-induced ferroelectric material within rk can act as a similar nucleus for further growth of the ferroelectric long-range order. It is as yet unclear, if the polar ZnO interface

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alone may also promote the relaxor to ferroelectric phase transition in the neighboring NBT-xBT grain [43]. This means that the volume of the transformed material in the present composite is not restricted to rk, since the growth of the long-range ordered ferroelectric phase can occur at stresses smaller than σ∗( . Moreover, it was shown that a time-dependent growth process can take place in NBT-xBT materials [44], which is not

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considered in the stress-temperature phase diagram. Another potential source of error is the oversimplified model with a spherical particle. Substantially higher stresses can be expected if the actual shape and the anisotropy of the ZnO grains were considered. The

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validity of the simple model, which does not consider the interaction of stress fields, was

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tested by computing σb in Table 1. For the composite with 0.1 mole fraction ZnO a low value of -29 MPa was computed, which is small in comparison to the critical transformation stress of -217 MPa. The small value of σb ascertains that the simplified model can serve as a first guideline for this composite. The simulation of composites with higher mole fractions may require more intricate modeling endeavors.

3.2. Temperature-Dependent Properties 3.2.1. Ferroelectric Properties 14

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The transition temperature from the induced long-range ordered ferroelectric state into the non-polar ergodic relaxor state (TF-R) serves as an upper bound for thermal depolarization

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[18,19]. An induced ferroelectric state is typically characterized by square-shaped polarization and butterfly-shaped strain loops, while the ergodic relaxor state is identified by slim polarization and sprout-shaped strain hysteresis loops with diminishing remanent

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polarization Prem and negative strain Sneg. The different shapes are exemplified in Figure 6a. The data indicate that at 110 °C the NBT-6BT is already in the ergodic phase (above TFwhile the NBT-6BT:0.1ZnO is still in the non-ergodic phase (below TF-R). Thus,

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R),

isothermal hysteresis loops were measured and evaluated in terms of Sneg to estimate the depolarization temperature. The results are depicted in Figure 6b. It is apparent that Sneg is highest for x = 0.1 at all temperatures and steadily diminishes with increasing ZnO content.

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For all compositions, Sneg decreases as a function of temperature with a rather pronounced drop between 90 °C for the pure NBT-6BT sample and 130 °C for the composite with x = 0.1.

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3.2.2. Dielectric Permittivity

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Figure 7a and b depict the real part of the relative dielectric permittivity (ε’) and the loss factor (tanδ) for poled samples, while the entire measured temperature range for poled and unpoled samples is shown in Figure S1. The data were acquired during heating from 80 to 160°C and measured at 10 kHz. The inflection point in Figure 7a, as well as the small peak in the loss factor (Figure 7b), defines the transition temperature from ferroelectric to ergodic relaxor (TF-R) [18,19]. For the NBT-6BT material without ZnO, the transition temperature was about 100 °C. It is evident that the transition range was broadened and 15

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shifted to higher temperatures for the composite materials. The temperature shift increases for x = 0.1 and then decreases with increasing ZnO content. For x = 0.1 this temperature

3.2.3. In situ Temperature-Dependent d33 Measurements

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can still be clearly determined and is equal to 138 °C.

In situ measurements of the piezoelectric coefficient as function of temperature d33(T) were

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used to determine Td as the inflection point of smoothed curves [17,19]. Figure 7 presents d33(T) in comparison to ε’(T) and tanδ(T). For NBT-6BT, the piezoelectric coefficient

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d33(T) first increases slightly as a function of temperature, followed by a sharp drop at Td (99 °C). For x = 0.1, Td is shifted by 37 °C to 136 °C. With further increase of the ZnO content, the depolarization temperature range broadens and Td decreases. This behavior is reflected in the ε’(T) and tanδ(T) data. It should be noted, that the flattening of the shoulder

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in ε’(T) does not necessarily indicate the absence of depolarization. However, an increased temperature stability of all composite samples as compared to NBT-6BT is evident. The magnitude of the obtained increase in depolarization temperature is deemed highly relevant

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for applications, as, for example, piezoelectric actuators in car engines are designed for a maximum temperature of 150 °C [45].

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Averaged values of the depolarization temperature are provided in Figure S2a. The average depolarization temperature increases from 99 °C for x = 0 to 136 °C for x = 0.1, but decreases with higher ZnO content to 125 °C for x = 0.4. The piezoelectric coefficient as a function of depolarization temperature is presented in Figure S2b. A trend of increasing piezoelectric properties with increasing Td is present in the composites. This tendency opposes the frequently reported inverse relationship between d33 and Td [20,21]. Zhang et al. related the increase in Td to a compensation of depolarization fields by the free charge 16

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carriers from ZnO [23]. Moreover, a depolarizing-effect-induced shift of the transition temperature is predicted for conventional ferroelectrics by the Landau-DevonshireGinzburg theory [46]. However, neither the presence of an electric bias field broadens the

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relative permittivity curves [19] nor does the Mn- or Fe-doping of NBT broaden in situ d33 profiles [47]. The influence of an uniaxial compressive stress on the temperature dependent relative permittivity and the piezoelectric coefficient has been studied in detail by Schader

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et al. in NBT-6BT [48]. He observed a broadening of the relative permittivity and d33 profiles with increasing uniaxial compressive stress, accompanied by a monotonic increase

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of TF-R, but a simultaneous decrease of Td.

In section 2.1.4. it was pointed out that an increase in TF-R can be achieved by deviatoric stresses stabilizing the non-cubic phase. However, the increase of TF-R due to stress fields does not necessarily imply a simultaneous increase of Td. For compressive stresses acting in

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direction of the poling axes [49,50], a local stress-induced reorientation of polarization vectors is observed, macroscopically depolarizing the material. Hence, three mechanisms are attributed to the incorporation of ZnO particles in this work. First, an increase of Td

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caused by a partial compensation of depolarization fields as proposed by the charge order

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model. Second, an increase in the ferroelectric to relaxor transition temperature (TF-R) due to deviatoric stresses. As the ferroelectric phase is energetically stabilized, this is expected to harden the domain structure and should also increase the depolarization temperature on a local scale. Third, an enhancement/reduction of the stability of the poled state if an uniaxial compressive stress acts perpendicular/parallel to the prior poling axis. This effect leads to a broad distribution of the driving force for a local stress-induced reorientation of

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polarization vectors and in turn to a broadening of the relative permittivity and d33(T) profiles.

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The influence of ZnO inclusions on the thermal depolarization of NBT-6BT is illustrated in Figure 8. Residual thermal stresses arise upon cooling from the sintering temperature due to a difference in CTE between ZnO and NBT-6BT, which puts the ZnO grains in compression. The model of a single particle in an infinite isotropic matrix predicts a

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homogeneous hydrostatic pressure σR in the ZnO particle and a declining deviatoric stress

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field with radial σr and tangential σt components in the NBT-6BT matrix, as depicted in Figure 8a. Within the critical radius rk the stress field is sufficient to induce ferroelectric long-range order as depicted in Figure 8b, while the rest of the matrix material still exhibits the pseudocubic structure. This transformed volume serves as a nucleus for a growth process, which is driven by the residual stress field, expanding the transformed volume

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beyond the critical radius rk. The application of an external poling field will reorient the direction of the polarization in this volume and thus induce a long-range ordered state in the

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remaining material (Figure 8c).

Considering polarization reorientation and phase transitions as possible mechanisms

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impacting depolarization, two different depolarization sequences may occur during the heating of a poled composite (Figure 8d). First, if the internal stresses are insufficient to affect the domain structure, the depolarization is governed by a detexturization of macroscopic ferroelectric domains [18].

Second, when stresses can affect the domain structure, then polarization reorientation and the detexturization of macroscopic domains contribute to the depolarization. Thereby, 18

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deviatoric stresses caused by the ZnO inclusions can increase the TF-R, which is expected to also increase the depolarization temperature. Normal stresses due to the ZnO particles will either promote or hinder the depolarization process depending on the orientation of the

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stress field with respect to the polarization axes (Figure 8e). Thus, it can be expected that the depolarization range broadens (Figure 7) in comparison to that of the single phase NBT6BT. Depolarization ultimately takes place when the phase transition occurs (Figure 8f).

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4. Conclusions

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An increase of the working temperature in lead-free Na1/2Bi1/2TiO3-based piezoelectric materials is deemed highly relevant for the substitution of lead-based piezoelectric materials. In this work, the upper limit of the working temperature of 0.94Na1/2Bi1/2TiO30.06BaTiO3:xZnO relaxor ferroelectric/semiconductor composites was quantified using

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dielectric, ferroelectric, and piezoelectric measurements. By varying the amount of ZnO the room temperature and temperature dependent properties can be altered in a controlled manner. Room temperature PFM and NMR data evidenced an induced ferroelectric long-

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range order in virgin samples. Thermal residual stresses can explain these findings indicating a stress-induced relaxor to ferroelectric transition.

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Temperature-dependent measurements of the relative dielectric permittivity, the piezoelectric coefficient d33, and the strain response revealed an increase in the depolarization temperature of the composites. This concurs with an enhancement (up to 37 °C) and a broadening of the temperature range in which depolarization takes place. Such a broadening is not observed for doped systems and can therefore be related to a stressinduced depolarization. The increase in depolarization temperature enhances the temperature stability, a fact that considerably widens the application spectrum for lead-free 19

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piezoceramics. From a more general perspective, thermal residual stresses via second phase inclusions are identified as generic tool to tune phase diagrams in functional materials. Acknowledgements

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The authors would like to thank Dietmar Gross for insightful discussion on the stressinduced phase stability. We are also thankful for valuable discussions with Yuri A. Genenko. Lalitha K.V. acknowledges and thanks the Alexander von Humboldt foundation for financial support.

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This work was supported by the Alexander von Humboldt foundation [grant numbers 3.5INI/1172830 STP, 2016]. References

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Figure Captions

Figure 1. X-ray diffraction profile of NBT-6BT: (a) full 2Θ range, (b) enlarged region between 33.5° and 37.5°. SEM micrographs of sintered, ground, and polished NBT-6BT:xZnO composites obtained in backscattered electron mode: (c) x=0.1, (d) x=0.4. A thermally etched specimen is presented in the inset (color on the Web only).

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Figure 2. Composition dependent bipolar strain (a-b) and polarization (c-d) hysteresis loops of unpoled samples measured at room temperature (virgin curves (a,c) and 3rd cycle (b,d). (c) Coercive field and (d) poling strain, and remanent strain extracted from bipolar polarization hysteresis loops of unpoled samples measured at room temperature. x denotes the molar ratio, while ϕZnO denotes the volume percentage of ZnO (color on the Web only).

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Figure 3. Surface topography (a,d,g), piezoresponse force microscopy amplitude (b,e,h) and phase (c,f,i) images of annealed NBT-6BT (a-c) and NBT-6BT:0.1ZnO (d-i) samples at room temperature. A weak contrast and no domain-related features for amplitude and phase images are visible for NBT-6BT (b-c) whereas blurry and lamellar regions with different contrast can be seen in the overview image (e-f) and around a single ZnO grain (h-i) of the NBT-6BT:0.1ZnO sample, which are not visible in the corresponding topography images (d,g). These domain-related structures indicate a locally induced ferroelectric order in unpoled composite samples, facilitated by the ZnO inclusion. The inset in g) provides the difference in the surface potential between the same ZnO grain and the NBT-6BT matrix measured by KPFM (color bar range: 207 mV). All scale bars are 1 µm. (color on the Web only). Figure 4. (a) 23Na MAS NMR spectra of two samples of NBT-6BT:xZnO with varying amount of ZnO. (b) Relative amount of cubic phase (bars) and ST/CT ratio (triangles) for two NBT-6BT:xZnO composite samples with different ZnO content (color on the Web only). Figure 5. (a) Thermal stress field of a spherical particle with the radius a in an infinite matrix, where r is the distance of a point to the center of the sphere, σR is the stress at the particle matrix interface and σr is the radial and σt the tangential component of the stress field in the matrix. (b) Two-dimensional projection of a three-dimensional reduced composite model with a spherical ZnO grain (dark) centered in a cube of NBT6BT matrix (bright). The experimentally determined particle radius a and the theoretical volume fraction of

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ZnO are used to calculate the dimension b of the cube. The critical radius of transformation rk estimates the amount of the stress-induced long-range ordered ferroelectric phase (striped). x denotes the mole ratio of ZnO (color on the Web only).

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Figure 6. (a) Difference between a “butterfly-shaped” (x=0.1) and a ”sprout-shaped” (x=0) isothermal strain hysteresis loop measured at 110 °C with a frequency of 1 Hz. (b) Negative strain extracted from isothermal bipolar strain hysteresis loops measured at different temperatures with a frequency of 1 Hz (color on the Web only). Figure 7. The temperature-dependent relative permittivity (a) and loss factor (b) are contrasted to the piezoelectric coefficient (c) (color on the Web only).

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Figure 8. Mechanism of thermal depolarization in (3-0)-type NBT-6BT:xZnO composites. (a) A stress field occurs due to the mismatch of the thermal expansion coefficients of a ZnO sphere and the NBT-6BT matrix. Here a is the particle radius, r is the distance of a point to the center of the sphere, σR is the stress at the particle matrix interface, σr is the radial and σt the tangential component of the stress field in the matrix, σr*is the critical transformation stress and rk the critical radius of transformation. (b) Stress induces a ferroelectric long-range order within rk leading to a growth process in the stress field. The remaining material is in the nonergodic relaxor state. (c) Electric poling leads to (d) a polarized composite. (e) At increased temperature, the local polarization switching in the vicinity of the ZnO sphere causes stepwise depolarization until (f) further heating leads to the ultimate depolarization due to the ferroelectric to relaxor transition.

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Table 1. Mole ratio (x), critical radius of transformation (rk), stress at the face center of the cube (σb) and volume fraction of induced long-ranged ordered phase (φT) of NBT-6BT:xZnO composites determined for ZnO grains in cubic coordination. ϕT / vol.%

2.4 4.9 7.3 9.8

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σb / MPa -29 -55 -80 -103

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rk / µm 0.41 0.40 0.47 0.46

x 0.1 0.2 0.3 0.4

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