Articleshttps://doi.org/10.1038/s41563-018-0034-4

Ultrahigh piezoelectricity in ferroelectric ceramics by designFei Li   1,2,5*, Dabin Lin1,5, Zibin Chen3,5, Zhenxiang Cheng4,5, Jianli Wang   4, ChunChun Li1, Zhuo Xu2, Qianwei Huang3, Xiaozhou Liao   3, Long-Qing Chen1*, Thomas R. Shrout1 and Shujun Zhang   1,4*

1Materials Research Institute, Pennsylvania State University, University Park, PA, USA. 2Electronic Materials Research Laboratory, Key Laboratory of the Ministry of Education, Xi’an Jiaotong University, Xi’an, China. 3School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney, Sydney, New South Wales, Australia. 4Institute for Superconducting and Electronic Materials, Australian Institute of Innovative Materials, University of Wollongong, Wollongong, New South Wales, Australia. 5These authors contributed equally: Fei Li, Dabin Lin, Zibin Chen and Zhenxiang Cheng. *e-mail: ful124@psu.edu; lqc3@psu.edu; shujun@uow.edu.au

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Supplementary Information for

Ultrahigh Piezoelectricity in Ferroelectric Ceramics by Design

Fei Li,1,2 Dabin Lin,1 Zibin Chen,3 Zhenxiang Cheng,4 Jianli Wang,4 ChunChun Li,1 Zhuo Xu,2

Qianwei Huang,3 Xiaozhou Liao,3 Long-Qing Chen,1 Thomas R. Shrout1 and Shujun Zhang1,4

1Materials Research Institute, Pennsylvania State University, University Park, PA 16802, USA

2Electronic Materials Research Laboratory, Key Laboratory of the Ministry of Education,

Xi’an Jiaotong University, Xi’an 710049, China 3School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney,

New South Wales 2006, Australia 4Institute for Superconducting and Electronic Materials, Australian Institute of Innovative Materials,

University of Wollongong, NSW 2500, Australia

Corresponding to: ful124@psu.edu (F.L.); lqc3@psu.edu (L.Q.C.); shujun@uow.edu.au (S.J.Z.)

Supplementary Figure 1│Temperature dependence of dielectric permittivity (a) and loss

factors (b) for PMN-28PT ceramics with different rare-earth and W dopants. The concentration

of dopants is 2 mol%. The data were measured at 1 kHz.

Supplementary Figure 2│The influence of Sm on the long-range ferroelectric phase of PMN-

PT. a, XRD patterns for PMN-31PT with different doping levels of Sm. b, enlarged (200)/(002)

patterns for PMN-31PT, which exhibits the phase evolution from pseudocubic to tetragonal phase by

adding Sm dopant. c, Phase diagram of 2.5 mol% Sm-doped PMN-xPT. d, Phase diagram of PMN-

xPT from this work and the reference [B. Noheda et al. Phys. Rev. B 66, 054104 (2002).]. Since Sm-

PMN-PT is a heterogeneous ferroelectric system, only the majority phase is marked in the phase

diagram for different compositions. Pseudocubic phase can be rhombohedral, monoclinic or mixed

of them.

Supplementary Figure 3│SEM images for PMN-PT and Sm-PMN-PT ceramics. The samples

are first polished and then thermally etched at temperature 200oC lower than their respective sintering

temperatures. The scale bar (white color) is 20 μm. Based on SEM images, the average grain size is

calculated by the Image Pro plus software.

4 8 12 16 20

Supplementary Figure 4│Synchrotron XRD patterns and refinement results for 2.5Sm-PMN-

31PT. a, 20 K; b, 130 K; c, 200 K; d, 310 K. The upper and lower data of the Bragg position represent

P4mm and Amm2, respectively.

Supplementary Figure 5│Domain structures for PMN-PT and Sm-PMN-PT ceramics by TEM

experiments. It is found that the domain structure is mainly associated with the long-range

ferroelectric phase for PMN-PT based ceramics. Therefore, if the long-range ferroelectric phase is

changed by the addition of Sm, as observed for PMN-31PT (R) and 2.5 mol% Sm-doped PMN-31PT

(T), the domain structure is significantly changed. While, if the long-range ferroelectric is not changed,

the variation of domain structural is minimal, as observed for PMN-36PT (T) and 2 mol% Sm-doped

PMN-36PT (T).

Supplementary Figure 6│TEM images of the 2.5Sm-PMN-31PT ceramic. a, Dark-field TEM

image. b, c, and d, Atomic-resolution TEM images for regions 1, 2 and 3 in a, respectively, recorded

along the crystallographic [001] direction; the polar vectors (arrows) are given for each unit cell

column. b and c show evidence of tetragonal-domain structures. d shows some heterogeneous polar

regions embedded in the tetragonal domain. Note that there are two regions with a significant

component of polarization perpendicular to the sample surface, and the direction of the perpendicular

component (inward or outward) cannot be determined by TEM. Here, they are plotted inward to the

paper.

Supplementary Figure 7│Temperature dependence of dielectric permittivity and loss factors

for PMN-29PT, PMN-31PT, PMN-34PT ceramics with various concentration of Sm. a, b, and c

are dielectric permittivity as a function of temperature for Sm-doped PMN-29PT, PMN-31PT and

PMN-34PT, respectively. d, e, and f are dielectric loss factor as a function of temperature for Sm-

doped PMN-29PT, PMN-31PT and PMN-34PT, respectively. The data were measured at 1 kHz.

Supplementary Figure 8│Low-temperature dielectric properties of classical ferroelectrics. a,

An [001]-oriented (K0.5Na0.5)NbO3 crystal; b, a Pb(Zr0.52Ti0.48)O3 ceramic. For the (K0.5Na0.5)NbO3

crystal, a rhombohedral-orthorhombic (R-O) phase transition is present around 150 K [Jaffe, B., Cook,

W. R., & Jaffe, H. Piezoelectric Ceramics (Academic Press, New York, 1971)]. As shown in the

figures, no phase-transition-unrelated dielectric loss maxima exist in Pb(Zr0.52Ti0.48)O3 or

(K0.5Na0.5)NbO3, since the nanoscale structural heterogeneity is minimal in these systems.

Supplementary Figure 9 │Dielectric permittivity of the 2.5Sm-PMN-31PT and PMN-36PT

ceramics with respect to temperature (∆T=T-TC). The inset shows the permittivity with respect to

temperature T.

Supplementary Figure 10 │ Dielectric behaviour of Ca- and Sr-doped PMN-31PT ceramics. a

and b, High- and low-temperature dielectric behaviour of the 2.5 mol% Ca-doped PMN-31PT

ceramic, respectively. c and d, High- and low-temperature dielectric behaviour of the 2.5 mol% Sr-

doped PMN-31PT ceramic, respectively. The data were measured at 1 kHz.

Supplementary Figure 11 │ Dielectric permittivity (at 1 kHz) as a function of temperature for

the 2.5 mol% Sm-doped PMN-29PT, PMN-31PT and PMN-34PT ceramics. According to the

XRD experiments, no ferroelectric phase transition was observed for the three ceramics below their

respective Curie temperatures.

Supplementary Figure 12 │Phase field simulations of the piezoelectric property for

PbZr0.6Ti0.4O3/PbZr0.2Ti0.8O3 supperlattices. a, 3D schematic of the supperlattices, where the green

and red colors represent rhombohedral PbZr0.6Ti0.4O3 and tetragonal PbZr0.2Ti0.8O3, respectively. The

thickness of one period is 8 nm. Fig. b illustrates the polar vectors on the XZ plane without

consideration of the interfacial interactions between rhombohedral and tetragonal PZTs while Fig. c

gives the polar vectors with consideration of the interfacial energies. Fig. d illustrates the polarization

rotation on the XZ-plane of a single domain PbZr0.6Ti0.4O3 (polarization along [111] direction) and

PbZr0.6Ti0.4O3/PbZr0.2Ti0.8O3 (n/m=6/2) under an electric field along the Z-direction (i.e., [001]). The

parameter n and m represent the thickness of rhombohedral and tetragonal PZT layers within a

superlattice, respectively. The color represents the angle between the polar vector and the [101]

direction. For a rhombohedral PZT, the projection of its polar vector on XZ-plane is along [101]

direction. Fig. e plots the electric-field-induced strains and the piezoelectric coefficient d33 for single

domain PbZr0.6Ti0.4O3/PbZr0.2Ti0.8O3 (n/m) supperlattices along the [001] direction showing the

dramatic influence of the embedded tetragonal layers within a superlattice. In the simulations, we

employed 64×64×64 discrete grid points and periodic boundary conditions.

It can be seen that tetragonal Pb(Zr0.2Ti0.8)O3 will transform to a rhombohedral phase to minimize the

interfacial energies, as shown in Fig. b&c. Compared to the homogeneous Pb(Zr0.6Ti0.4)O3, the

addition of Pb(Zr0.2Ti0.8)O3 layers facilitates the polarization rotation process under an applied [001]

electric field and thus enhances the piezoelectricity, as show in Fig. d&e. The reason for the enhanced

piezoelectricity is due to the competition between the interfacial and ferroelectric bulk energies, being

analogous to that proposed in Sm-PMN-PT ceramics.

Supplementary Figure 13 │Aging experiments for Sm-doped PMN-PT ceramics with

comparison of PZT ceramics. After poling, the relative variations of dielectric permittivity as a

function of time are measured. a, 2.5Sm-PMN-29PT ceramics; b, 2.5Sm-PMN-31PT ceramics; c,

“soft” and “hard” PZT ceramics. For the aging measurements, the samples are first annealed at 900oC,

then poled by electric fields of 10 kV cm-1 at room temperature. To each Sm-PMN-PT composition,

three samples are used for aging measurements, where the standard errors are given in the figures.

Supplementary Table 1│Electromechanical properties of various Sm-doped PMN-PT ceramics.

Composition d33

(pC N-1)

k33 ε/ε0 tanδ TC

(oC)

Pr

(μC cm-2)

EC

(kV cm-1)

1%Sm-PMN-28PT 420 0.72 2500 0.022 118 23 3.2

1%Sm-PMN-29PT 460 0.72 2800 0.020 120 24 3.5

1%Sm-PMN-30PT 560 0.73 3300 0.020 125 26 3.7

1%Sm-PMN-31PT 550 0.74 3700 0.018 136 26 4.0

1%Sm-PMN-32PT 710 0.77 4100 0.018 141 27 4.2

1%Sm-PMN-34PT 780 0.76 5100 0.015 148 26 5.5

1%Sm-PMN-36PT 700 0.75 4800 0.015 157 28 5.9

2%Sm-PMN-28PT 900 0.75 5100 0.025 95 22 2.8

2%Sm-PMN-29PT 1050 0.77 7500 0.024 102 24 3.0

2%Sm-PMN-30PT 1000 0.79 8000 0.020 107 25 2.8

2%Sm-PMN-31PT 1100 0.79 8300 0.020 113 25 3.2

2%Sm-PMN-32PT 1050 0.80 9000 0.017 118 24 3.6

2%Sm-PMN-34PT 780 0.72 6300 0.018 125 24 5.3

2%Sm-PMN-36PT 480 0.67 4000 0.016 136 26 5.3

2.5%Sm-PMN-28PT 1320 0.77 12500 0.035 85 21 2.3

2.5%Sm-PMN-29PT 1510 0.78 13000 0.035 89 23 2.3

2.5%Sm-PMN-30PT 1350 0.77 11000 0.025 97 24 2.6

2.5%Sm-PMN-31PT 1250 0.79 10000 0.019 104 23 3.3

2.5%Sm-PMN-32PT 1000 0.75 8000 0.015 109 22 3.9

2.5%Sm-PMN-34PT 710 0.72 5800 0.016 120 24 4.2

2.5%Sm-PMN-36PT 450 0.69 4000 0.018 129 26 4.9

3%Sm-PMN-28PT 1200 0.70 15000 0.051 69 19 1.7

3%Sm-PMN-29PT 1420 0.71 15000 0.038 73 20 2.1

3%Sm-PMN-30PT 1250 0.72 12000 0.026 78 21 2.5

3%Sm-PMN-31PT 980 0.69 10000 0.020 88 20 3.2

3%Sm-PMN-32PT 800 0.71 7200 0.015 95 21 3.5

3%Sm-PMN-34PT 610 0.68 4700 0.016 106 22 3.5

3%Sm-PMN-36PT 400 0.65 3900 0.017 117 24 3.7

Supplementary Table 2│Density of Sm-doped PMN-PT ceramics. The lattice parameters used for

calculation of the theoretical densities are from XRD results. The measured densities are from the

average of five samples and the corresponding errors are given in brackets.

PMN-29PT PMN-31PT PMN-34PT

Doping

level

(mol%)

0 1 2 3 0 1 2 3 0 1 2

Measured

density

(g cm-3)

7.93

(0.03)

7.85

(0.04)

7.81

(0.03)

7.75

(0.03)

7.95

(0.02)

7.87

(0.02)

7.83

(0.03)

7.75

(0.04)

7.88

(0.02)

7.83

(0.02)

7.81

(0.03)

Theoretical

Density

(g cm-3)

8.14 8.11 8.06 8.03 8.15 8.12 8.09 8.05 8.16 8.13 8.09

Relative

density 97.4% 96.8% 96.9% 96.5% 97.5% 96.9% 96.8% 96.3% 96.5% 96.3% 96.5%

Supplementary Table 3│Rietveld-refinement parameters for 2.5Sm-PMN-31PT. For P4mm, there is one A-site (0, 0, 0), one B-site (0.5, 0.5, Z) and

two O-sites: O1 (0.5, 0.5, Z) and O2 (0.5, 0, Z). For Amm2, there is one A-site (0, 0, 0), one B-site (0, 0.5, Z), and two O-sites: O1 (0, 0, Z) and O2 (X,

0.5, Z). For Pm-3m, there is one A-site (0, 0, 0), one B-site (0.5, 0.5, 0.5) and one O-site (0.5, 0.5, 0).

Temp. 20 K 80 K 130 K 200 K 250 K 310 K 350 K 380 K 410 K 450 K

Information of

tetragonal

P4mm phase

Volume

fraction (%) 75.91 74.61 75.54 76.40 79.80 91.71 94.85 35.50 0 0

a (Å) 3.9994(1) 4.0000(1) 4.0016(1) 4.0019(1) 4.0038(1) 4.0064(1) 4.0084(1) 4.0097(1) / /

c (Å) 4.0424(2) 4.0419(2) 4.0405(1) 4.0402(1) 4.0368(1) 4.0311(1) 4.0281(1) 4.0152(1) / /

Z(Ti/Mg/Nb) 0.5242(2) 0.5224(2) 0.5172(3) 0.5151(3) 0.5075(5) 0.5034(18) 0.5014(11) 0.5009(12) / /

ZO1 0.0800(4) 0.0765(4) 0.0759(4) 0.0753(5) 0.0716(6) 0.0423(10) 0.0393(8) 0.0360(9) / /

ZO2 0.5750(4) 0.5699(4) 0.5686(4) 0.5686(5) 0.5685(4) 0.5559(8) 0.5424(40) 0.5387(10) / /

Information of

orthorhombic

Amm2 phase

Volume

fraction (%) 24.09 25.39 24.46 23.60 20.20 8.29 5.15 0 0 0

a (Å) 5.6934(2) 5.6935(2) 5.6943(2) 5.6926(2) 5.6914(3) 5.6889(1) 5.6856(3) / / /

b (Å) 3.9958(1) 3.9961(2) 3.9973(4) 4.0004(3) 4.0026(3) 4.0053(3) 4.0057(4) / / /

c (Å) 5.6797(3) 5.6802(2) 5.6805(3) 5.6794(4) 5.6809(4) 5.6812(3) 5.6819(2) / / /

Z(Ti/Mg/Nb) 0.492(3) 0.490(4) 0.501(3) 0.494(7) 0.498(6) 0.487(1) 0.501(9) / / /

ZO1 0.496(21) 0.490(9) 0.509(7) 0.505(7) 0.507(18) 0.507(30) 0.533(19) / / /

XO2 0.242(13) 0.247(7) 0.232(3) 0.232(2) 0.226(5) 0.240(4) 0.259(20) / / /

ZO2 0.253(16) 0.244(8) 0.242(2) 0.247(3) 0.267(5) 0.287(9) 0.295(20) / / /

Information of

cubic phase

Volume

fraction (%) 0 0 0 0 0 0 0 64.50 100 100

a (Å) / / / / / / / 4.01359(3) 4.01439(3) 4.01503(2)

Rp (%) 3.94 3.92 3.98 4.05 3.74 5.28 4.98 4.21 5.29 5.2

Rwp (%) 5.60 5.57 5.73 5.90 5.46 7.15 6.63 5.46 7.55 7.3

Supplementary Table 4│Dielectric and piezoelectric properties for a batch of 2.5Sm-PMN-

29PT ceramics. For the averaged values, standard errors are given in brackets.

sample 1 2 3 4 5 average

ε33/ε0 13200 13500 13800 12900 13100 13300 (300)

d33 (pC N-1) 1550 1520 1530 1450 1490 1508 (40)

Supplementary Table 5│Dielectric and piezoelectric properties for a batch of 2.5Sm-PMN-

31PT ceramics. For the averaged values, standard errors are given in brackets.

sample 1 2 3 4 5 average

ε33/ε0 10300 10500 10600 10200 9800 10280 (190)

d33 (pC N-1) 1230 1270 1260 1250 1220 1246 (20)