Available online at www.sciencedirect.com Journal of the European Ceramic Society 32 (2012) 4341–4352 Structural phase transitions and electrical properties of (KxNa1−x)NbO3-based ceramics modified with Mn Henry E. Mgbemere a , Manuel Hinterstein b , Gerold A. Schneider a,∗ a Institute of Advanced Ceramics, Hamburg University of Technology, Denickestraße 15, 21073 Hamburg, Germany Institut für Werkstoffwissenschaft, Technische Universität Dresden, Helmholtzstraße 7, 01069 Dresden, Germany b Received 28 March 2012; received in revised form 4 July 2012; accepted 26 July 2012 Available online 13 August 2012 Abstract (K0.5 Na0.5 )NbO3 (KNN) ceramics and KNN containing Li, Ta modified with 2 mol% of manganese have been produced using the mixed-oxide ceramics synthesis route. The structure and properties of these piezoelectric ceramics modified with manganese have been investigated using high resolution X-ray diffraction and electrical characterisation. The structural information about the ceramics was determined by Rietveld refinement with Fullprof. The phase transition temperatures observed with X-ray diffraction compares well with the values from dielectric studies. The addition of Mn slightly reduced the phase transition temperatures and for the sample containing only Li, the phase changed from orthorhombic to monoclinic phase with space group Pm. The dielectric, piezoelectric and ferroelectric properties of the samples decreased with Mn addition due to hard doping effects resulting from oxygen vacancies in the perovskite lattice. © 2012 Elsevier Ltd. All rights reserved. Keywords: Powders-solid state reaction; X-ray methods; Ferroelectric properties; Perovskites; Actuators 1. Introduction Researches into lead-free KNN-based piezoelectric ceramics have increased in the last 10 years because of the need to find piezoelectric ceramic compositions with good piezoelectric properties and are also environmentally harmless. The properties of unmodified KNN ceramics have been reported in the literature.1,2 It has a high Curie temperature (Tc ) ∼420 ◦ C, phase boundaries which resemble the morphotropic phase boundary in Pb(Zrx Ti1−x )O3 (PZT) ceramics but a low piezoelectric coefficient (∼80 pC/N) and other electromechanical properties which do not meet the requirements for industrial applications. Substitution in KNN ceramics with isovalent elements has been used by many researchers to improve both the piezoelectric properties and the sintering process. When used in their optimum amounts to dope KNN ceramics, Sb,3 Li,4,5 Ta6 alone or in combination7–11 have all been reported to improve the piezoelectric properties. ∗ Corresponding author. Tel.: +49 04042878 3037; fax: +49 04042878 2647. E-mail address: g.schneider@tu-harburg.de (G.A. Schneider). 0955-2219/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jeurceramsoc.2012.07.033 Manganese is an interesting element because of its multivalent ions (Mn2+ , Mn3+ , Mn4+ ) and its ability to improve sintering, resistivity and quality mechanical factor (Qm ) of piezoelectric ceramics. It acts as a domain pinning element in Pb(Mg1/3 Nb2/3 )O3 ceramics12 and with more than 0.5 wt.% in Pb(Zr1−x Tix )O3 –Pb(Zny Nb1−y )O3 ceramics, densification deteriorates and the crystal structure changes from tetragonal to rhombohedral.13 It changes the crystal structure from tetragonal to rhombohedral in (Bi0.5 Na0.5 )TiO3 –BaTiO3 (BNT–BT) ceramics14–17 and the piezoelectric response decreases with ≥0.8 wt.%.16 In a BNT single crystal with increasing amounts of Mn, the sequence of phase transition is not altered but the transition temperature is lowered.17 Based on results of the dielectric, piezoelectric and electromechanical properties, Mn is believed to enter both A- and B-sites of the lattice in (CaSr)Bi4 Ti4 O15 ceramics.18 The Mn3+ is believed to play a critical role in the soft and hard doping effects. When used to dope BaTiO3 ceramics (0.5–1.7 mol%), the crystal structure changes from tetragonal to hexagonal.19 Jahn Teller distortions by Mn3+ Ti were proposed to be the driving force for the phase transition. Mn also promotes densification and slightly lowers the remanent polarisation (Pr ) and coercive field (Ec ) in (Kx Na1−x )NbO3 ceramics.20 Decreased leakage current and high current densities 4342 H.E. Mgbemere et al. / Journal of the European Ceramic Society 32 (2012) 4341–4352 Table 1 OES-ICP data and the calculated molar amounts of the elements in the samples. Mn O Zr* – – – – 271 3 <0.5 <0.00075 581 (16) 0.98 – – 6.4 (1) 0.01917 284 2.92174 <0.5 <0.00075 120 (1) 0.4827 577 (1) 0.98 – – 6.04 (1) 0.01794 286 2.91646 0.5 0.0009 66.4 (3) 0.51723 113 (7) 0.51689 423 (5) 0.81487 109 (1) 0.10812 5.69 (1) 0.01853 270 3.02436 <0.5 <0.00075 66.3 (4) 0.50017 115 (17) 0.5088 476 (35) 0.88784 113 (8) 0.10845 5.57 (6) 0.01757 272 2.94419 0.5 0.00075 Element Li Na K Nb (K0.5 Na0.5 )NbO3 OES-ICP values (g/kg) Element amount (mol) – – 78.1 (2) 0.53737 125 (2) 0.50682 587 (8) 1 (K0.50 Na0.50 )(Nb0.98 Mn0.02 )O3 – OES-ICP values (g/kg) Element amount (mol) – 72.7(1) 0.49523 121 (1) 0.48469 (K0.48 Na0.48 Li0.04 )(Nb0.98 Mn0.02 )O3 OES-ICP values (g/kg) 1.52 (1) Element amount (mol) 0.03446 72.6 (3) 0.49853 (K0.50 Na0.50 )(Nb0.88 Ta0.1 Mn0.02 )O3 OES-ICP values (g/kg) – – Element amount (mol) (K0.48 Na0.48 Li0.04 )(Nb0.88 Ta0.1 Mn0.02 )O3 1.28 (8) OES-ICP values (g/kg) Element amount (mol) 0.03198 are the results of doping KNN single crystals with Mn.21,22 When used to dope (K0.5 Na0.5 )0.935 Li0.065 NbO3 ceramics, no significant change on the crystal structure was observed and hard ferroelectric effects were observed due to oxygen vacancies.23 A change of valence state from Mn4+ to Mn3+ has been observed using synchrotron X-ray absorption spectroscopy for (K0.5 Na0.5 Li0.065 )NbO3 doped with Mn and the phase was identified to be tetragonal.24 With 0.8 mol% Mn in 0.98(K0.5 Na0.5 )NbO3 –0.02(BiScO3 ) ceramics, the optimum values of piezoelectric and dielectric properties were obtained.25 Both acceptor and donor doping effects and phase coexistence are reported in Mn-doped 0.94(K0.5 Na0.5 )NbO3 –0.06Ba(Zr0.05 Ti0.95 )O3 ceramics.26 Most of these studies on Mn doped KNN-based ceramics mainly concern electrical properties. There is very little information on its effect on the structure and phase coexistence in these KNN ceramics. Synchrotron diffraction was used in this work to study the effect of Mn doping on the structure of KNN based ceramics. The objective of this work therefore, is to study the effect of Manganese on KNN-based ceramics and to correlate the results of structural studies with the electrical properties of these ceramics. 2. Experimental details 2.1. Sample preparation The compositions intended to be produced are (K0.5 Na0.5 )NbO3 , (K0.50 Na0.50 )(Nb0.98 Mn0.02 )O3 , (K0.48 Na0.48 Li0.04 )(Nb0.98 Mn0.02 )O3 , (K0.50 Na0.50 )(Nb0.88 Ta0.1 Mn0.02 )O3 , (K0.48 Na0.48 Li0.04 ) (Nb0.88 Ta0.1 Mn0.02 )O3 . K2 CO3 , Na2 CO3 , Li2 CO3 (99%), Nb2 O5 and Ta2 O5 (99.9%) (Chempur Feinchemikalien und Forschungs GmbH, Karlsruhe, Germany) and MnO2 (Merck chemicals Darmstadt, Germany) are the raw powders used for the synthesis. The powders were first dried in the oven at 220 ◦ C for 4 h to remove any moisture present. Stoichiometric amounts of the starting oxide-based Ta powders were measured while 2 mol% excess powders were added for the carbonates. The powders were milled using an attrition mill operating at 500 rpm for 2 h with ethanol as solvent and 3 mm Ø zirconia balls as grinding media. Solvent extraction was carried out to separate the ethanol from the powder while the powders were calcined at 850 ◦ C for 4 h with a heating rate of 3 ◦ C/min. The milling process was repeated to homogenise the powders and to reduce the average particle size of the powders to below 1 ␮m. A cold isostatic press operating at 300 MPa was used to press the samples for 2 min. The samples were sintered in air for 1 h with a heating rate of 2 ◦ C/min and a cooling rate of 10 ◦ C/min at different temperatures as indicated in the brackets [(K0.5 Na0.5 )NbO3 1085 ◦ C, (K0.50 Na0.50 )(Nb0.98 Mn0.02 )O3 1060 ◦ C, (K0.48 Na0.48 Li0.04 ) (Nb0.98 Mn0.02 )O3 1050 ◦ C, (K0.50 Na0.50 )(Nb0.88 Ta0.1 Mn0.02 )O3 1085 ◦ C, (K0.48 Na0.48 Li0.04 ) (Nb0.88 Ta0.1 Mn0.02 )O3 1070 ◦ C]. The densities of the samples were measured using the Archimedes method. The samples for chemical analysis and synchrotron diffraction measurements were ground and annealed at 900 ◦ C for 4 h. The samples were polished while those used for microstructural investigations were chemically etched using Mastermet (Al2 O3 -based suspension) and also thermally etched at 950 ◦ C for 30 min at 10 ◦ C/min heating and cooling rates. The grain size measurements were determined using the mean intercept length method from a minimum of six different area of the micrograph. The samples were poled at room temperature with a field of 2 kV/mm. Polarisation hysteresis measurements were carried out at room temperature using the standard Sawyer–Tower circuit and a complete dipolar hysteresis measurement was performed in 200 s. Unipolar strain hysteresis measurement was used to determine the piezoelectric ∗ ) values. coefficient (d33 Optical emission spectroscopy-inductive coupled plasma (OES-ICP (PE-Optima 7000 DV)) analysis was used to determine quantitatively the amount of each element present. A mean value was obtained from four separate measurements and the element amounts in moles are shown in Table 1. Small amounts of H.E. Mgbemere et al. / Journal of the European Ceramic Society 32 (2012) 4341–4352 some elements were lost while a small amount of Zr was introduced through the grinding balls made from ZrO2 . The slight increase in the amounts of some elements could be due to their presence as impurities in other powders. The final compositions were adjusted to reflect the changes observed after the chemical analysis. Finally, the actual compositions were adjusted to be: (K0.507 Na0.537 )NbO3 (K0.485 Na0.495 )(Nb0.98 Mn0.019 )O2.92 (K0.483 Na0.499 Li0.04 )(Nb0.98 Mn0.018 )O2.96 (K0.517 Na0.517 )(Nb0.815 Ta0.108 Mn0.019 )O3.024 (K0.509 Na0.5 Li0.032 )(Nb0.888 Ta0.108 Mn0.018 )O2.944 (KNN) (KNN-2Mn) (KNNLi-2Mn) (KNNTa-2Mn) (KNNLiTa-2Mn) 2.2. Synchrotron X-ray data collection and refinement The X-ray data were collected at the synchrotron facility (beamline B2, HASYLAB/DESY) in Hamburg from 26 ◦ C to 500 ◦ C in steps of either 10 ◦ C or 20 ◦ C. High temperature measurements were performed using a capillary furnace from Stoe & Cie type 0.65.3 and the data were recorded on heating by a position sensitive image plate detector (OBI, ortsfest auslesbarer Bildplattendetektor)27 at a wavelength of 0.6881 Å. More details about the experimental setup at the beamline can be found in the literature.27,28 All the collected data were analysed by the Rietveld refinement method using the Fullprof software.29 The background under the peaks was refined using a linear interpolation between points from the regions in which no reflections contributed to the intensity. The model used was based on a T–C–H pseudoVoigt profile function which is convoluted with asymmetry due to axial divergence as formulated by Laar and Yelon30 and using the method of Finger et al.31,32 The atomic positions and the isotropic atomic displacement parameters Biso were refined. The anisotropic peak broadening model in the general strain formulation from Stephens was used to refine the strain in the sample.33 2.3. Temperature-dependent measurement of dielectric properties The dielectric property measurements were carried out from room temperature to temperatures above the respective Tc of the samples. The surfaces of the pellets were coated with silver paints which acted as electrodes for the dielectric measurements. The measurements were done with an LCR meter (HP 4284A, Agilent Technologies, Inc., Palo Alto, USA) connected to a heating chamber at 5 ◦ C The dielectric properties plots were made with data obtained at a frequency of 100 kHz. 3. Results and discussion 3.1. Structural characterisation Fig. 1 shows the measured and calculated diffraction profiles and the difference curves taken at 27 ◦ C for KNN-based ceramics modified with Mn. KNN, KNN-2Mn and KNNTa-2Mn samples in Fig. 1a, b and d, respectively, have orthorhombic symmetry 4343 at 27 ◦ C, while KNNLi-2Mn (Fig. 1c) has monoclinic symmetry and KNNLiTa-2Mn (Fig. 1e) has a two-phase coexistence between an orthorhombic and a tetragonal phase. The inset in each figure shows the enlarged section of the patterns with higher 2θ regions (35–55◦ ). The refinement was carried out from 27 ◦ C to temperatures above the respective Tc of the samples. In order to show the difference between the orthorhombic and the monoclinic phase, an enlargement of the patterns between 2θ angles (19–24◦ ) is shown in Fig. 2 and a representation of the two structures is shown in Fig. 3. The clear splitting of the 200c reflection at ∼20◦ shows a threefold splitting for KNNLi-2Mn which means that all three axes in the pseudo-cubic cell are of different length. This indicates at least orthorhombic symmetry. A ferroelectric orthorhombic structure like Amm2 is setup in a way so that the bo and co axes are the [1 1 0]c axes (Fig. 3a). / co this results in a rhombic distortion of the (0 0 1)c If bo = plane with two equal apc (or [1 0 0]c ) axes. To reproduce the resulting angle α together with three different 1 0 0c directions, monoclinic symmetry is necessary. In this case we used P11m with the mirror plane perpendicular to the c-axis and gamma (γ) as the monoclinic angle (Fig. 3b). The effect of the monoclinic angle can be observed at the 110c reflection in Fig. 2. It shows a fourfold splitting into 1 1 0, −1 1 0, 1 0 1 and 0 1 1. The setup of the P11m space group shows that the atomic positions in the a–b plane are restricted due to the mirror plane perpendicular to the c-axis. Therefore the polar displacement is only possible in the mirror plane and the refinement results in an alignment close to the [1 1 0]c direction. The angle γ results in the rhombic distortion of the (0 0 1)c plane but due to the monoclinic setup, the 1 0 0c reflection is not equal to the 0 1 0c but the structure still shows a pseudo-orthorhombic character. Orthorhombic, tetragonal, monoclinic and cubic phases were observed with changes in temperature and space groups Amm2, P4mm, Pm and Pm3̄m, respectively, were used for the refinement. Single phase and sometimes mixed phases were observed in the diffraction patterns. When phase coexistence is observed, two-phase refinement models which are a combination of the space groups involved were used. The refinement parameters for KNN, KNN-2Mn, KNNLi-2Mn, KNNTa-2Mn and KNNLiTa2Mn ceramics for the lowest temperatures of each model used are shown in Tables 2, 3, 4, 5 and 6, respectively. Fig. 4 shows the lattice parameters of the samples as a function of temperature. The subscripts ‘o’, ‘t’, ‘m’ and ‘c’ represent the orthorhombic, tetragonal, monoclinic and cubic phases, respectively. The orthorhombic cell parameters bo and co were divided by (2)1/2 for better representation in the diagrams. The plot for KNN ceramics (Fig. 4a) shows that from 27 ◦ C to 180 ◦ C, only the orthorhombic phase is present and between 200 ◦ C and 220 ◦ C, a coexistence of an orthorhombic and a tetragonal phase is present. From 240 ◦ C to 400 ◦ C the tetragonal phase exists, with coexistence between the cubic and the tetragonal phase at 420 ◦ C. Above 420 ◦ C, the cubic phase is observed. The plot for KNN-2Mn ceramics (Fig. 4b) shows that the orthorhombic phase is present up to 160 ◦ C and from 180 ◦ C to 200 ◦ C, orthorhombic–tetragonal coexistence is observed. The tetragonal phase is present from 220 ◦ C to 420 ◦ C, and above this temperature, the cubic phase is present. 4344 H.E. Mgbemere et al. / Journal of the European Ceramic Society 32 (2012) 4341–4352 10000 5000 80000 80000 10000 0 5000 60000 -5000 -10000 40000 -15000 35 40 45 50 Measured Calculated Error Amm2 55 2 theta [°] 20000 0 -5000 Intensity [a.u] Intensity [a.u] 60000 40000 Measured Calculated Error P11m -10000 -15000 35 20000 40 45 50 55 2 theta [°] 0 0 -20000 -20000 10 20 (a) 30 40 50 10 60 20 (c) 2 theta [°] 30 40 50 60 2 theta [°] 5000 60000 0 50000 -5000 60000 -10000 30000 -15000 35 20000 40 45 50 55 2 theta [°] 10000 0 Measured Calculated Error Amm2 Intensity [a.u] 40000 Intensity [a.u] 5000 80000 0 -5000 -10000 40000 -15000 35 20000 40 45 50 55 Measured Calculated Error Amm2 2 theta [°] 0 -10000 -20000 10 (b) 20 30 40 50 -20000 60 10 20 (d) 2 theta [°] 30 40 50 60 2 theta [°] 5000 50000 0 40000 -5000 Intensity [a.u] 30000 -10000 20000 -15000 35 10000 40 45 50 55 2 theta [°] Measured Calculated Error Amm2 P4mm 0 -10000 -20000 (e) 10 20 30 40 50 60 2 theta [°] Fig. 1. Measured and calculated X-ray diffraction profiles and their difference plot at 27 ◦ C for (a) KNN, (b) KNN-2Mn, (c) KNNLi-2Mn, (d) KNNTa-2Mn and (e) KNNLiTa-2Mn ceramics. Fig. 4c shows the lattice parameters for KNNLi-2Mn ceramics. The monoclinic phase is present from 27 ◦ C to 70 ◦ C and between 80 ◦ C and 150 ◦ C, a mixture of monoclinic and tetragonal phase is observed. From 160 ◦ C to 440 ◦ C, only the tetragonal phase is present and from 450 ◦ C, the cubic phase is present. For the KNNTa-2Mn sample (Fig. 4d), the orthorhombic phase is present from 27 ◦ C to 140 ◦ C and orthorhombic–tetragonal phase coexistence is observed from 160 ◦ C to 180 ◦ C. The tetragonal phase is present from 200 ◦ C to 360 ◦ C while a tetragonal–cubic phase coexistence is present from 380 ◦ C to 400 ◦ C and at 420 ◦ C, the cubic phase is present. The plot for the KNNLiTa-2Mn sample (Fig. 4e) shows orthorhombic–tetragonal phase coexistence from 27 ◦ C to 140 ◦ C and from 160 ◦ C to 360 ◦ C, only the tetragonal phase is observed. The cubic phase is observed from 380 ◦ C and above. In Amm2, the different values of the orthorhombic lattice parameters bo and co lead to a rhombic distortion of the (0 0 1)c plane resulting in an expansion along [1 1 0]c . The plot of the pseudo-monoclinic angle as a function of temperature for samples with the orthorhombic phase is shown in Fig. 5. As the 4345 H.E. Mgbemere et al. / Journal of the European Ceramic Society 32 (2012) 4341–4352 Table 2 Experimental details and refinement results for KNN at 27, 200, 240, 420 and 440 ◦ C. Phase type Single Two-phase Crystal system Space group Temperature (◦ C) Orthorhombic Amm2 27 Orthorhombic Amm2 200 a (Å) b (Å) c (Å) V (g/cm−3 ) Z Refinement RB (%) Rf (%) GOF χ2 No. of parameters 3.94455(3) 5.64377(4) 5.67647(4) 126.3705(15) 2 3.95598(3) 5.64421(6) 5.66918(6) 126.584(2) 2 5.37 4.82 4.5 20.6 29 4.9 3.83 4.4 19.5 36 Single Two-phase Tetragonal P4mm Tetragonal P4mm 240 Tetragonal P4mm 420 Cubic Pm3̄m Cubic Pm3̄m 440 3.96372(5) – 4.02863(7) 63.2941(16) 1 3.96471(2) – 4.02684(3) 63.2976(7) 1 3.97726(3) – 4.00854(4) 63.4094(9) 1 3.98679(3) – – 63.3678(9) 1 3.986603(18) – – 63.3591(5) 1 5.89 5.22 4.8 23.1 28 7.71 7.98 4.7 22.1 28 7.5 6.39 – – – Single 4.75 3.79 – – – 11.1 12.5 6 36.3 19 Table 3 Experimental details and refinement results for KNN-2Mn at 27, 180, 220 and 420 ◦ C. Phase type Single Two-phase Crystal system Space group Temperature (◦ C) Orthorhombic Amm2 27 Orthorhombic Amm2 180 a (Å) b (Å) c (Å) V (g/cm−3 ) Z Refinement RB (%) Rf (%) GOF χ2 No. of parameters 3.94514(3) 5.64309(5) 5.67440(5) 126.3278(19) 2 3.95503(4) 5.64372(7) 5.66869(7) 126.532(2) 2 5.92 5.53 3.9 15.2 31 5.45 4.4 3.8 14.3 36 Single Single Tetragonal P4mm 180 Tetragonal P4mm 220 Cubic Pm3̄m 420 3.96390(8) – 4.02631(14) 63.263(3) 1 3.96391(2) – 4.02730(3) 63.2794(7) 1 3.98607(3) – – 63.3336(7) 1 6.61 6.64 4.1 16.1 31 7.33 6.4 5.8 34.2 26 7.31 6.05 – – – Table 4 Experimental details and refinement results for KNNL-2Mn ceramics at 27, 80, 170, 450 and 460 ◦ C. Phase type Single Two-phase Crystal system Space group Temperature (◦ C) Monoclinic P11 m 27 Monoclinic P11 m 80 a (Å) b (Å) c (Å) γ (◦ ) V (g/cm−3 ) Z Refinement RB (%) Rf (%) GOF χ2 No. of parameters 4.01097(4) 3.98931(4) 3.94495(3) 89.6881(6) 63.1223(11) 1 4.01379(5) 3.98693(6) 3.94842(3) 89.7182(7) 63.1846(13) 1 5.31 4.6 4.1 17.1 36 4.72 3.58 4.4 19.4 47 Single Two-phase Tetragonal P4mm 80 Tetragonal P4mm 170 Tetragonal P4mm 450 Cubic Pm3̄m 450 Cubic Pm3̄m 460 3.95549(10) – 4.02963(18) – 63.047(4) 1 3.959406(20) – 4.03278(3) – 63.2214(6) 1 3.97763(8) – 4.00474(17) – 63.361(3) 1 3.986710(20) – – – 63.3642(5) 1 3.986167(16) – – – 63.3383(4) 1 5.43 5.1 4.8 23.3 33 4.73 5.75 4.8 22.7 32 10 9.77 – – – 6.53 7.21 5.1 25.9 21 8.43 5.95 – – – Single 4346 H.E. Mgbemere et al. / Journal of the European Ceramic Society 32 (2012) 4341–4352 Table 5 Experimental details and refinement results for KNNT-2Mn ceramics at 27, 140, 200, 380 and 420 ◦ C. Phase type Single Two-phase Crystal system Space group Temperature (◦ C) Orthorhombic Amm2 27 Orthorhombic Amm2 140 Tetragonal P4mm 140 a (Å) b (Å) c (Å) V (g/cm−3 ) Z Refinement RB (%) Rf (%) GOF χ2 No. of parameters 3.94846(4) 5.63831(6) 5.66623(7) 126.145(2) 2 3.95607(4) 5.63893(7) 5.66222(7) 126.313(3) 2 3.9627(2) – 4.02745(2) 63.245(5) 1 4.89 4.62 4.1 16.6 34 5.11 3.63 4.3 18.4 29 11.7 6.99 – – – Single Two-phase Tetragonal P4mm 200 Tetragonal P4mm 380 3.96453(3) 3.97731(5) Single Cubic Pm3̄m 380 Cubic Pm3̄m 420 3.98384(2) – – 63.2272(7) 1 5.94 6.38 4.9 24.5 20 – – 4.01762(4) 63.1471(9) 1 4.0005(2) 63.284(4) 1 3.98400(5) – – 63.2349(14) 1 5.69 4.49 20.4 4.5 29 7.08 6.74 4.9 24.3 27 5.54 5.99 – – – Table 6 Experimental details and refinement results for KNNLT-2Mn ceramics at 27, 140 and 400 ◦ C. Phase type Two-phase Crystal system Space group Temperature (◦ C) Orthorhombic Amm2 27 a (Å) b (Å) c (Å) V (g/cm−3 ) Z Refinement RB (%) Rf (%) GOF χ2 No. of parameters 3.94760(5) 5.63459(10) 5.66034(9) 125.903(3) 2 KNNLi-2Mn 200 002 200 020 0,5 011 1,0 -110 101 KNN 110 Intensity [a.u] 1,5 002 2,0 022 111 5.27 4.33 4.0 16.1 36 0,0 14 20 2-theta [°] Fig. 2. Enlarged section of the diffraction patterns showing the difference in 1 1 0c and 2 0 0c reflections between the KNN ceramics (orthorhombic phase) and the KNNLi-2Mn ceramics (monoclinic phase). Single Single Tetragonal P4mm 27 Tetragonal P4mm 140 Cubic Pm3̄m 400 3.95606(9) – 4.0079(2) 62.726(4) 1 3.95875(3) – 4.01800(4) 62.9688(10) 1 3.98034(2) – 5.15 4.75 – – – 5.64 4.39 4.2 17.4 31 7.32 7.78 4.6 21.2 20 63.0610(6) 1 temperature increases, the pseudo-monoclinic angles decrease in the following order: KNN, KNN-2Mn, KNNLi-2Mn, KNNTa2Mn and KNNLiTa-2Mn. As the pseudo-monoclinic angle decreases, the tendency to form the orthorhombic lattice increases. The percentages of each phase present in the samples are calculated through their scale factors which comprise a product of mass and volume of the unit cell of each phase. The weight fraction of the phases in percentage is presented in Fig. 6 . The temperature range of phase coexistence for KNN, KNN-2Mn and KNNTa-2Mn in Fig. 5a, b and d, respectively, are narrow and are restricted to the phase transition region. For KNN and KNNTa-2Mn samples, the tetragonal phase and the cubic phase also coexist close the Tc of the samples. For KNNLi-2Mn sample (Fig. 6c) at 70 ◦ C, only the monoclinic phase is present and as the temperature increases the monoclinic phase decreases while the phase is completely tetragonal at 160 ◦ C. For KNNLiTa2Mn (Fig. 6e) sample, approximately 70% of the orthorhombic phase is present up to 60 ◦ C and above this temperature; there is a gradual decrease in this phase while the tetragonal phase increases up to 100% at 160 ◦ C. H.E. Mgbemere et al. / Journal of the European Ceramic Society 32 (2012) 4341–4352 4347 Fig. 3. Graphical representation of the orthorhombic structure model Amm2 and the monoclinic structure model Pm used in the refinements. The arrow indicates the direction of spontaneous polarisation (PS ). The SEM images of the polished and etched surfaces of the samples are shown in Fig. 7. In all the samples, the grains and the pores can be clearly seen with the latter located mainly at the grain boundary junctions. The grinding and polishing process is believed to have contributed to some of the pores through grain pull-out. For KNN ceramics (Fig. 7a), grains with smooth and rough surfaces are observed and this is possibly due to different crystallographic planes. A steeped/rough surface results when the higher energetic planes try to revert to the lower energetic planes. The KNN sample has small grains and the average grain size is 1.8 ± 1.0 ␮m. The average grain size of the samples increases with the addition of 2 mol% Mn. The average grain size for KNN-2Mn (Fig. 7b) ceramics is 5.5 ± 2.4 ␮m while it is 8.0 ± 3.5 ␮m for KNNLi-2Mn (Fig. 7c). The average size for KNNTa-2Mn (Fig. 7d) is 3.3 ± 1.5 ␮m while it is 3.0 ± 1.3 ␮m for KNNLT-2Mn ceramics. A few big grains and many small grains are observed for KNNLT-2Mn ceramics. 3.2. Electrical characterisation The dielectric constant values of the samples as a function of temperature are shown in Fig. 8a and the insets highlight the low temperature part of the graph which shows the ferroelectric–ferroelectric phase transition. With the exception of the KNN sample, the other samples show signs of a diffuse phase transition at their dielectric peak. The phase transition temperatures observed for the samples at the Tc with X-ray diffraction are similar to those from dielectric measurements as shown in Table 7. The only exception is the KNNTa-2Mn sample with a difference of up to 30◦ . It should be pointed out that at 360 ◦ C a mixture of cubic and tetragonal phase is present in the diffraction pattern. The KNNLiTa-2Mn sample has the highest dielectric constant and lowest dielectric loss at temperatures below 100 ◦ C. The tetragonal to orthorhombic phase transition temperature (TT–O ) for the KNN sample is ∼207 ◦ C while the Tc occurred at 421 ◦ C with a dielectric peak value of ∼3740. For KNN-2Mn sample, the TT–O is 192 ◦ C while the Tc occurred at 421 ◦ C with a dielectric peak value of ∼4855. The monoclinic to orthorhombic transition temperature (TM–O ) for KNNLi-2Mn sample is at 105 ◦ C while the Tc occurred at 453 ◦ C with a dielectric peak of ∼4601. The TT–O for KNNTa2Mn sample is ∼160 ◦ C while the Tc occurred at 362 ◦ C with a dielectric peak of ∼4145 and the TT–O for KNNLiTa-2Mn sample is ∼83 ◦ C while the Tc occurred at 403 ◦ C with a dielectric peak of ∼3285. The plot of dielectric loss values (Fig. 8b) shows that the KNN sample has the highest dielectric loss value below 120 ◦ C. The presence of Li and Ta in the ceramic seems to play a role in the loss values because the KNN-2Mn sample has higher loss values between 120 ◦ C and 250 ◦ C. The polarisation hysteresis curves for the samples in Fig. 9 show that 2 mol% Mn reduces the ferroelectric activity in the samples. The KNN sample looks to be slightly conductive and show a Pr value of ∼25 ␮C/cm2 with a coercive field of ∼12 kV/cm. The Pr and Ec values of the doped samples are strongly reduced possibly due to the high content of Mn. It is not clear if the curve for KNN-2Mn sample indicate the presence of ferroelectricity. The decreasing value of both Ec and Pr indicates both soft and hard doping effects occurring in the samples. The relative density of the sintered samples is shown in Table 7 and they indicate good values for samples sintered in air. The piezoelectric coefficient of the samples obtained from the slope ∗ values of the unipolar strain hysteresis curves show that low d33 are obtained compared to when there is no Mn present.9 3.3. Discussion The result of chemical analysis using OES-ICP shows that the amounts of Li, K and Mn are slightly lower than expected in some samples. This is possibly due to their high vapour pressure which makes them to be volatile during the sintering process. It also shows that synthesis of polycrystalline ceramics which involves milling of powders is not completely free of impurities. The A- and B-site elements have valence states of +1 and +5, respectively, while oxygen has −2. Based on the result from electron paramagnetic studies on KNN ceramics, Mn is believed to be incorporated to the B-site of the perovskite lattice.21,23 It therefore acts as an acceptor and the possible defect chemical 4348 H.E. Mgbemere et al. / Journal of the European Ceramic Society 32 (2012) 4341–4352 KNNLi-2Mn KNN 4,04 4,04 ct 1/2 4,02 co/(2 ) 4,00 bo/(2 ) Lattice parameter (Å) Lattice parameter (Å) ct 1/2 ac 3,98 at 4,00 bm ac 3,98 at cm 3,96 3,96 ao 3,94 3,94 0 50 100 150 (a) 200 250 300 350 400 450 0 500 Lattice parameter (Å) 1/2 1/2 bo/(2 ) ac at 3,98 3,96 Temperature [°C] KNNTa-2Mn ct co/(2 ) 4,00 100 150 200 250 300 350 400 450 500 550 4,04 KNN-2Mn 4,02 50 (c) Temperature [°C] 4,04 Lattice parameter (Å) am 4,02 ct 4,02 1/2 co/(2 ) 4,00 1/2 3,98 at ao 3,96 ao 3,94 ac bo/(2 ) 3,94 50 0 (b) 100 150 200 250 300 350 400 450 500 0 4,04 100 150 200 250 300 350 400 450 Temperature [°C] KNNLiTa-2Mn ct 4,02 Lattice parameter (Å) 50 (d) Temperature [°C] 4,00 1/2 co/(2 ) 3,98 ac 1/2 bo/(2 ) at ao 3,96 3,94 0 50 100 (e) 150 200 250 300 350 400 450 Temperature [°C] Fig. 4. Lattice parameters (Å) of the samples as a function of temperature. ao , bo and co represent the parameters for the orthorhombic phase, am , bm and cm represents the parameters for the monoclinic phase, at and ct represent the parameters for the tetragonal phase while ac represents the cubic phase, respectively. The graphs are for (a) KNN ceramic, (b) KNN-2Mn, (c) KNNLi-2Mn, (d) KNNTa-2Mn and (e) KNNLiTa-2Mn. reactions for +3 and +4 valence states are shown in Eqs. (1) and (2), respectively. 2ABO ′′ Mn2 O3 −→3 2Mn 2ABO •• B + 3O× O + 2VO •• 2MnO2 −→3 2Mn′B + 4O× O + VO (1) (2) Oxygen vacancies are formed and when they combine with Mn ions, defect dipoles are created. These defect dipoles move along the direction of polarisation and are based on the principle of symmetry conforming of point defects and lead to hard doping effects.34 The phase transition temperatures of the samples are lowered with doping and this is possibly due to the introduction of inhomogeneous electric field generated by the vacancies created.35 The X-ray diffraction patterns for KNN, KNN2Mn and KNNTa-2Mn samples show that at 27 ◦ C, only the 4349 H.E. Mgbemere et al. / Journal of the European Ceramic Society 32 (2012) 4341–4352 Table 7 ∗ ), first order transition temperature and Curie temperature (T ) for KNN-based ceramics modified with Mn. Relative density, piezoelectric coefficient (d33 c Sample ∗ (pm/V) d33 Relative density (%) KNN KNN-2Mn KNNLi-2Mn KNNTa-2Mn KNNLiTa-2Mn 94.5 92.4 92.1 95 93 ± ± ± ± ± 1.5 1 1 0.5 0.5 100 119 147 205 152 ± ± ± ± ± 15 11 15 12 10 Pseudomonoclinic angle [°] 90,35 90,30 90,25 90,20 KNN KNN-2Mn KNNTa-2Mn KNNLT-2Mn KNNLi-2Mn 90,15 0 50 100 150 200 250 Temperature [°C] Fig. 5. Pseudo-monoclinic angles as a function of temperature for KNN, KNN2Mn, KNNLi-2Mn, KNNTa-2Mn and KNNLiTa-2Mn ceramics. The angle for KNNLi-2Mn was obtained by subtracting the monoclinic angles from 180◦ to ensure a uniform plot. orthorhombic phase is present. The sequence of phase transitions with increasing temperature is also similar; from the orthorhombic phase to the tetragonal phase and finally to the cubic phase, but the difference lies in the temperature of phase transitions. Mn appears to have very little effect on the phase coexistence of TT–O or TM–O (◦ C) Tc (◦ C) Dielectric X-ray Dielectric 207 192 105 160 83 420–440 420–440 440–450 400–420 380–400 421 421 453 362 403 the KNNLiTa-2Mn sample because the sequence and temperature of the phase transitions are similar with and without it.9 Composition fluctuation which in a way is due to compositional inhomogeneities is believed to be the main reason for phase coexistence in the samples.36 The change in slope of the lattice parameters observed at certain temperatures for the samples correspond to a phase transition. KNN ceramics modified with Li has an orthorhombic structure at 27 ◦ C9 but when 2 mol% of Mn is introduced, a monoclinic phase with space group Pm is formed from 27 ◦ C to 70 ◦ C. This monoclinic phase also coexists with the tetragonal phase from 80 ◦ C to 150 ◦ C. A possible reason for the structural phase transition is the lattice instability due to forces which determine the interaction of the ions being displaced. A possible change in the valence state of Mn from +4 to +3 introduces a pseudo-Jahn Teller effect which is related to low symmetry distortion of the lattice.37 When Mn is added to KNN containing Ta (KNNTa-2Mn), the phase did not change possibly because the lattice instability introduced is low. When Nb and Ta have the same coordination number, the values of their ionic radius are similar. At temperatures below 100 ◦ C, KNN-2Mn had the lowest ∗ dielectric constant values which corresponds with the low d33 values and the poor hysteresis curve. KNNLiTa-2Mn ceramic has the highest permittivity values below 100 ◦ C and this may Fig. 6. Weight fraction of the phases (%) as a function of temperature for (a) KNN, (b) KNN-2Mn, (c) KNNLi-2Mn, (d) KNNTa-2Mn and (e) KNNLiTa-2Mn ceramics. 4350 H.E. Mgbemere et al. / Journal of the European Ceramic Society 32 (2012) 4341–4352 Fig. 7. Scanning electron microscope (SEM) images of the polished and etched surfaces of (a) KNN, (b) KNN-2Mn, (c) KNNLi-2Mn, (d) KNNTa-2Mn and (e) KNNLT-2Mn ceramics. be due to phase coexistence. Although a new monoclinic phase with Pm space group is observed for KNNLi-2Mn sample, the dielectric properties did not greatly improve. The coexistence of the monoclinic and the tetragonal phase over a wide temperature range also did not lead to a significant improvement in the dielectric constant values probably because of the hard doping effects. The diffuseness of the dielectric constant peaks at the phase transition temperatures of the samples is mainly due to an increase in site disorder as a result of the doping in the samples. The energy barriers decrease due to the vacancies and promote enhanced fluctuations between the energy minima below the Tc . The addition of Mn to the samples also led to a reduction in the dielectric loss values compared to KNN sample which had higher loss values. Relatively high Pr is obtained for the KNN sample and it is clear that there is a small contribution due to leakage current to the curve. When Mn is added to the samples, low Pr values are obtained. The shape of the curve for KNN-2Mn indicates that the ferroelectric behaviour in the sample has been greatly lowered. This is probably because the rate of migration of the defects due to doping is low and this creates an inner biased field which tends to reverse the switched polarisation. A pinning of the domains is created because the defect dipoles do not respond to the motion of the polarisation as fast as possi∗ ble. There is no difference in the piezoelectric coefficient d33 values for KNN and KNN-2Mn samples. Although a new Pm ∗ value phase is obtained for KNNLi-2Mn composition, the d33 is not very high while the KNNTa-2Mn sample gave the highest values. The KNNLiTa-2Mn composition has a two-phase coexistence between the orthorhombic and the tetragonal phase but ∗ is not high which may be explained by the fact the value of d33 that although there is phase coexistence, the degree of defects introduced by doping with 2 mol% Mn may have affected the properties adversely. H.E. Mgbemere et al. / Journal of the European Ceramic Society 32 (2012) 4341–4352 KNN KNN-2Mn KNNLi-2Mn KNNTa-2Mn KNNLiTa-2Mn 5000 Dielectric constant 4000 1200 800 3000 400 2000 0 50 100 150 200 250 Temperature [°C] 1000 0 0 100 200 (a) 300 400 500 Temperature [°C] 6 KNN KNN-2Mn KNNLi_2Mn KNNTa_2Mn KNNLiTa-2Mn 0,15 tan δ 0,10 amounts were less than intended due to their high vapour pressure during sintering and also that small amounts of impurities are always introduced during processing. A new monoclinic phase with Pm space group is obtained with the KNNLi-2Mn sample from 27 ◦ C to about 150 ◦ C probably due to the Jahn Teller effect on Mn in valence changes from +4 to +3. Mn is believed to be incorporated to the B-site of the perovskite lattice and this leads to the formation of oxygen vacancies. When these O2− vacancies combine with Mn ions, defect dipoles are created and because they do not respond fast enough to the movement of the domains, they pin the domains leading to hard ferroelectric effects. An inner biased field is also believed to be formed which tends to reverse the switched polar∗ , dielectric constant and isation leading to low values of Pr , d33 dielectric loss. The phase transition temperatures of the samples are lowered probably due to inhomogeneous electric field generated by the vacancies. Acknowledgements 4 The research leading to these results has received financial support from Deutsche Forschungsgemeinschaft under Grant No. SCHN 372/16-2 and the Bundesministerium für Bildung und Forschung under Grant No. 05K10ODA. 0,05 2 0,00 4351 0 50 100 150 200 250 Temperature [°C] References 0 0 100 200 300 400 500 Temperature [°C] (b) Fig. 8. Temperature-dependent plots of (a) dielectric constant and (b) dielectric loss (tan δ) measured at 100 kHz for KNN-based ceramics doped with Mn. 30 2 Polarisation [µC/cm ] 20 10 0 -10 KNN KNN-2Mn KNNLi-2Mn KNNTa-2Mn KNNLT-2Mn -20 -30 -20 -10 0 10 20 Electric Field [kV/cm] Fig. 9. Polarisation – electric field hysteresis curves for KNN-based ceramics modified with Mn. 4. Conclusion The effect of Mn doping on the structure and piezoelectric properties of KNN-based ceramics has been investigated. The chemical analysis on the samples shows that Li, K and Mn 1. Egerton L, Dillion DM. Piezoelectric and dielectric properties of ceramics in the system potassium–sodium niobate. J Am Ceram Soc 1959;42(9):438–42. 2. Jaeger RE, Egerton L. Hot pressing of potassium–sodium niobates. J Am Ceram Soc 1962;45(5):209–13. 3. Mgbemere HE, Schneider GA, Stegk TA. Effect of antimony substitution for niobium on the crystal structure, piezoelectric and dielectric properties of (K0.5 Na0.5 )NbO3 ceramics. Funct Mater Lett 2010;3(1):25–30. 4. Klein N, Hollenstein E, Damjanovic D, Trodahl HJ, Setter N. A study of the phase diagram of (K,Na,Li)NbO3 determined by dielectric and piezoelectric measurements, and Raman spectroscopy. J Appl Phys 2007;102(1):014112. 5. Guo Y, Kakimoto K-I, Ohsato H. Phase transitional behavior and piezoelectric properties of (Na0.5 K0.5 )NbO3 –LiNbO3 ceramics. Appl Phys Lett 2004;85(18):4121–3. 6. Matsubara M, Yamaguchi T, Kikuta K, Shin-Ichi H. Synthesis and characterization of (K0.5 Na0.5 )(Nb0.7 Ta0.3 )O3 piezoelectric ceramics sintered with sintering Aid K5.4 Cu1.3 Ta10 O29 . Jpn J Appl Phys 2005;44:6618–23. 7. Saito Y, Takao H. High performance lead-free piezoelectric ceramics in the (K,Na)NbO3 –LiTaO3 solid solution system. Ferroelectrics 2006;338:17–32. 8. Guo Y, Kakimoto K-I, Ohsato H. (Na0.5 K0.5 )NbO3 –LiTaO3 lead-free piezoelectric ceramics. Mater Lett 2005;59(2–3):241–4. 9. Mgbemere HE, Hinterstein M, Schneider GA. Electrical and structural characterization of (Kx Na1−x )NbO3 ceramics modified with Li and Ta. J Appl Crystallogr 2011;44:1080–9. 10. Mgbemere HE, Herber R-P, Schneider GA. Investigation of the dielectric and piezoelectric properties of potassium sodium niobate ceramics close to the phase boundary at (K0.35 Na0.65 )NbO3 and partial substitutions with lithium and antimony. J Eur Ceram Soc 2009;29:3273–8. 11. Hollenstein E, Davis M, Damjanovic D, Setter N. Piezoelectric properties of Li and Ta modified (K0.5 Na0.5 )NbO3 ceramics. Appl Phys Lett 2005;87:182905. 12. Park J-H, Park J-G, Kim B-K, Je H-J, Kim Y. Effect of MnO2 addition on the piezoelectric properties in Pb(Mg1/3 Nb2/3 )O3 relaxor ferroelectrics. Mater Res Bull 2002;37(2):305–11. 4352 H.E. Mgbemere et al. / Journal of the European Ceramic Society 32 (2012) 4341–4352 13. Lee S-M, Lee S-H, Yoon C-B, Kim H-E, Lee K-W. Low-temperature sintering of MnO2 -doped PZT–PZN piezoelectric ceramics. J Electroceram 2007;18(3–4):311–5. 14. Aksel E, Jakes P, Erdem E, Smyth DM, Ozarowski A, Tol JV, et al. Processing of manganese-doped [Bi0.5 Na0.5 ]TiO3 ferroelectrics: reduction and oxidation reactions during calcination and sintering. J Am Ceram Soc 2011;94(5):1363–7. 15. Li X-J, Wang Q, Li Q-L. Effects of MnO2 addition on microstructure and electrical properties of (Bi0.5 Na0.5 )0.94 Ba0.06 TiO3 ceramics. J Electroceram 2008;20(2):89–94. 16. Fan G, Lu W, Wang X, Liang F. Effects of manganese additive on piezoelectric properties of (Bi1/2 Na1/2 )TiO3 –BaTiO3 ferroelectric ceramics. J Mater Sci 2007;42(2):472–6. 17. Ge W, Li J, Viehland D, Luo H. Influence of Mn doping on the structure and properties of Na0.5 Bi0.5 TiO3 single crystals. J Am Ceram Soc 2010;93(5):1372–7. 18. Li G, Zheng L, Yin Q, Jiang B, Cao W. Microstructure and ferroelectric properties of MnO2 -doped bismuth-layer (Ca,Sr)Bi4 Ti4 O15 ceramics. J Appl Phys 2005;98(6):064108. 19. Langhammer HT, Mueller T, Felgner K-H, Abicht H-P. Crystal structure and related properties of manganese-doped barium titanate ceramics. J Am Ceram Soc 2000;83(3):605–11. 20. Lin D, Kwok KW, Chan HLW. Piezoelectric and ferroelectric properties of Kx Na1−x NbO3 lead-free ceramics with MnO2 and CuO doping. J Alloys Compd 2008;461(1–2):273–8. 21. Kizaki Y, Noguchi Y, Miyayama M. Defect control for low leakage current in K0.5 Na0.5 NbO3 single crystals. Appl Phys Lett 2006;89(14):142910. 22. Noguchi Y, Miyayama M. Effect of Mn doping on the leakage current and polarization properties in K0.14 Na0.86 NbO3 ferroelectric single crystals. J Ceram Soc Jpn 2010;118:711–6. 23. Zuo R, Fu J, Su S, Fang X, Cao J-L. Electrical properties of manganese modified sodium potassium lithium niobate lead-free piezoelectric ceramics. J Mater Sci Mater Electron 2009;20(3):212–6. 24. Wongsaenmai S, Kanchiang K, Chandarak S, Laosiritaworn Y, Rujirawat S, Yimnirun R. Crystal structure and ferroelectrics of Mndoped ((K0.5 Na0.5 )0.935 Li0.065 )NbO3 lead-free ceramics. Curr Appl Phys 2012;12(2):418–21. 25. Li X, Jiang M, Liu J, Zhu J, Zhu X, Zhu J, et al. Enhanced piezoelectric properties in Mn-doped 0.98 K0.5 Na0.5 NbO3− 0.02BiScO3 lead-free ceramics. J Am Ceram Soc 2009;92(7):1625–8. 26. Lin D, Kwok KW, Chan HLW. Effects of MnO2 on the microstructure and electrical properties of 0.94(K0.5 Na0.5 )NbO3 –0.06Ba(Zr0.05 Ti0.95 )O3 leadfree ceramics. Mater Chem Phys 2008;109(2–3):455–8. 27. Knapp M, Joco V, Baehtz C, Brecht HH, Berghaeuser A, Ehrenberg H, et al. Position-sensitive detector system OBI for high resolution X-ray powder diffraction using on-site readable image plates. Nucl Instrum Methods Phys Res A 2004;521(2–3):565–70. 28. Knapp M, Baehtz C, Ehrenberg H, Fuess H. The synchrotron powder diffractometer at beamline B2 at HASYLAB/DESY: status and capabilities. J Synchrotron Radiat 2004;11(4):328–34. 29. Rodríguez-Carvajal J. Recent advances in magnetic structure determination by neutron powder diffraction. Phys B: Condens Matter 1993;192(1–2):55–69. 30. Laar BV, Yelon WB. The peak in neutron powder diffraction. J Appl Crystallogr 1984;17:47–54. 31. Finger LW, Cox DE, Jephcoat AP. A correction for powder diffraction peak asymetry due to axial divergence. J Appl Crystallogr 1994;27: 892–900. 32. Finger LW. PROFVAL: functions to calculate powder-pattern peak profiles with axial divergence asymmetry. J Appl Crystallogr 1998;31:111. 33. Stephens PW. Phenomenological model of anisotropic peak broadening in powder diffraction. J Appl Crystallogr 1999;32:281–9. 34. Lin D, Guo MS, Lam KH, Kwok KW, Chan HLW. Lead-free piezoelectric ceramic (K0.5 Na0.5 )NbO3 with MnO2 and K5.4 Cu1.3 Ta10 O29 doping for piezoelectric transformer application. Smart Mater Struct 2008;17(3):035002. 35. Bellaiche L, Íñiguez J, Cockayne E, Burton BP. Effects of vacancies on the properties of disordered ferroelectrics: a first-principles study. Phys Rev B 2007;75:014111. 36. Frantti J, Ivanov S, Eriksson S, Rundlöf H, Lantto V, Lappalainen J, et al. Phase transitions of Pb(Zrx Ti1−x )O3 ceramics. Phys Rev B 2002;66(6):064108. 37. Aksenov VL, Plakid NM, Stamenkovic S [Pontekorvo DB, Trans.] Neutron Scattering by Ferroelectrics. World Scientific 1989:1–67.