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1
Transparent Ferroelectric Crystals with Ultrahigh Piezoelectricity 1
Chaorui Qiu,
1†
Bo Wang,
2†
Nan Zhang,
1†
Shujun Zhang,
3,2
Jinfeng Liu,
1
David Walker,
4
Yu Wang,
5
2
Hao Tian,
5
Thomas R. Shrout,
2
Zhuo Xu,
1*
Long-Qing Chen
2*
and Fei Li
1*
3
1
Electronic Materials Research Lab, Key Lab of Education Ministry/International Center for Dielectric 4
Research, School of Electronic and Information Engineering, State Key Laboratory for Mechanical 5
Behavior of Materials, Xi’an Jiaotong University, Xi’an, 710049, China 6
2
Materials Research Institute, Department of Materials Science and Engineering, The Pennsylvania 7
State University, University Park, PA, 16802, USA 8
3
ISEM, Australian Institute for Innovative Materials, University of Wollongong, Wollongong, NSW 9
2500, Australia 10
4
Department of Physics, University of Warwick, Coventry CV4 7AL, UK
11
5
School of Physics, Harbin Institute of Technology, Harbin 150001, China 12
13
†
These authors contributed equally 14
*
Corresponding authors (Z.X.: xuzhuo@xjtu.edu.cn; L.Q.C: lqc3@psu.edu; F.L.: ful5@xjtu.edu.cn) 15
16
Transparent piezoelectrics are highly desired for numerous hybrid ultrasound-optical devices ranging 17
from photoacoustic imaging transducers to transparent actuators for haptic applications
1,2,3,4,5,6,7
. 18
However, it has long been challenging to simultaneously achieve high piezoelectricity and perfect 19
transparency, since most high-performance piezoelectrics are ferroelectrics that contain high-density 20
light-scattering domain walls. Here, through a combination of phase-field simulations and experiments, 21
we demonstrate a relatively simple method of using an AC electric-field to engineer the domain 22
structures of originally opaque rhombohedral Pb(Mg
1/3
Nb
2/3
)O
3
-PbTiO
3
(PMN-PT) crystals to 23
simultaneously generate near-perfect transparency, ultrahigh piezoelectric coefficient d
33
(>2100 pC N
-
24
1
), outstanding electromechanical coupling factor k
33
(~94%), and large electro-optical coefficient γ
33
25
(~220 pm V
-1
), far beyond the performance of the commonly used transparent ferroelectric crystal 26
LiNbO
3
(d
33
~ 40 pC N
-1
, k
33
~ 47%, and γ
33
~ 30 pm V
-1
). We find that increasing the domain sizes 27
leads to a higher value of d
33
for the [001]-oriented rhombohedral PMN-PT crystals, challenging the 28
conventional wisdom that decreasing the domain sizes always results in higher piezoelectricit
8,9,10
. This 29
work presents a paradigm to achieve an unprecedented combination of properties and functionalities 30
through ferroelectric domain engineering, and the new transparent ferroelectric crystals reported here 31
are expected to open up a wide range of hybrid device applications, such as medical imaging, self-32
energy-harvesting touch screens and invisible robotic devices. 33
34
35
36
2
Achieving simultaneous high piezoelectricity and perfect transparency in a piezoelectric material has 37
long been a great challenge. For example, traditional high-performance piezoelectric transducers are 38
typically made from perovskite ferroelectric ceramics and crystals with chemical compositions around 39
their morphotropic phase boundaries (MPBs), e.g., Pb(Zr,Ti)O
3
(PZT) ceramics and domain-40
engineered Pb(Mg
1/3
Nb
2/3
)O
3
-PbTiO
3
(PMN-PT) crystals. These materials possess very high d
33
and k
33
41
11,12,13,14
, but they are usually opaque in the visible light spectrum. On the other hand, the commonly 42
used transparent piezoelectrics, LiNbO
3
crystals and polyvinylidine fluoride (PVDF) polymers
6,7
, have 43
good transparency but much lower values of d
33
and k
33
(LiNbO
3
:
d
33
<40 pC N
-1
, k
33
~ 47%; PVDF:
d
33
44
~ 20 pC N
-1
, k
33
~ 16%), which severely limit the acoustic source level, bandwidth, and sensitivity of 45
the transparent transducers. 46
In addition to the extrinsic effects, such as porosity and grain boundaries which exist ubiquitously in 47
ceramics, the poor transparency in PZT ceramics and domain-engineered PMN-PT crystals is closely 48
associated with the light scattering and reflection by their ferroelectric domain walls. One can think of 49
two possible approaches to reduce the light-scattering domain walls. The first is to pole a ferroelectric 50
crystal along the polar direction to achieve a single-domain state. However, the value of d
33
for such 51
single-domain PMN-PT crystals is generally very low,
13,14
much below that of [001] poled multi-52
domain rhombohedral PMN-PT crystals (>1500 pC N
-1
). In principle, one can first pole a 53
rhombohedral PMN-PT crystal along the [111] direction to achieve a single domain state with good 54
transparency, then rotate the crystal to [001] direction to guarantee the high longitudinal 55
piezoelectricity. However, this approach is not feasible in practice as detailed in the Methods section. 56
The second approach is to dramatically reduce the domain sizes by breaking the domains into polar 57
nanoregions whose spatial sizes (a few to tens of nanometres) are much smaller than the wavelength of 58
visible light, thus greatly improving the light transparency as observed in La-doped PZT
15,16
. However, 59
improving the transparency using polar nanoregions was achieved at the expense of a drastically 60
reduced remanent polarization and thus very low values of d
33
. Therefore, optical functionalities in 61
high-performance piezoelectrics have not been realized despite more than 50 years of efforts. 62
In this work, we show that one can use AC electric-fields to effectively eliminate light-scattering 71° 63
domain walls for [001]-oriented rhombohedral PMN-PT crystals to achieve both near-perfect 64
transparency and ultrahigh piezoelectricity. We first perform phase-field simulations to study the 65
domain evolution of a [001]-oriented 0.72Pb(Mg
1/3
Nb
2/3
)O
3
-0.28PbTiO
3
(PMN-28PT) rhombohedral 66
crystal using both conventional DC and AC electric-fields. We generate the initial pristine unpoled state 67
starting from a random distribution of small polarizations representing a high-temperature paraelectric 68
state. The obtained multi-domain state contains all eight possible <111> rhombohedral domain variants 69
with an average size of ~ 20 nm. Three types of domain walls are present in the unpoled rhombohedral 70
crystal, i.e., 71
o
, 109
o
and 180
o
domain walls. 71
Under a DC electric-field along the [001] direction, the four domain variants with polarizations along 72
[111
], [1
11
], [1
1
1
] or [11
1
] are switched to the [111], [11
1], [1
1
1] or [1
11] directions. Thus, 73
only 71
o
and 109
o
domain walls survived while the 180
o
domain walls were eliminated by poling, as 74
3
shown Fig. 1a. The horizontal layers are separated by a set of 109° domain walls parallel to the (001) 75
plane, while within each lamina, there are 71° domain walls approximately parallel to {011} planes. It 76
should be noted that 71° domain walls can scatter light since the refractive indices n
o
and n
e
(the 77
subscript letters ‘o’ and ‘e’ represent ordinary and extraordinary light, respectively) change as light 78
travels across a 71° domain wall, as shown in Extended Data Fig. 1. In contrast, 109° domain walls do 79
not induce light scattering since the refractive indices are the same for the domains on both sides of a 80
109° domain wall. 81
Our phase-field simulations demonstrate that the application of an AC electric-field effectively reduces 82
the number of 71° domain walls with only two 71
o
domain walls left in each lamina after AC-poling, 83
leading to the much larger domain size within each lamina. To understand the reason for the 84
elimination of 71° domain walls by AC-poling, we analyse the domain evolution during the 85
polarization reversal process, as shown in Fig. 1b and SI Videos 1&2. One can see that the reversal of 86
electric field causes the “swinging” of 71
o
domain walls, i.e., 71
o
domain walls alternating between 87
(011) and (011
) planes. During this process, the contiguous 71° domains tend to merge with each other, 88
and thus a significant increase in 71
o
domain size after AC-poling. In addition, as presented in Extended 89
Data Fig. 2, the total free energy of the system is reduced during AC-poling since the energies arising 90
from the discontinuities of polarization/strain associated with domain walls decrease as the domain 91
wall density decreases. In other words, alternating the polarity of the electric-field back and forth 92
lowers the free energy of a ferroelectric crystal, leading to a domain structure with reduced domain 93
wall density. As discussed above, due to the significantly decreased 71° domain wall density, the light 94
transmission of the AC-poled sample is expected to be superior to a corresponding DC-poled sample. 95
Following the phase-field simulations, we characterized the domain structures of AC-poled and DC-96
poled PMN-28PT crystals. Using birefringence imaging microscopy (BIM)
17
, we characterized the 97
orientation (φ) of the principal axis of the optical indicatrix projected on the (001) planes, as shown in 98
Fig. 2a. For a rhombohedral single domain, the projection of the optical axis is along the face diagonal. 99
Therefore, the orientation φ of a rhombohedral domain would be 45° or 135°, which are represented by 100
blue and red colours respectively, as shown by the colour bar in Fig. 2a. A multi-domain crystal may 101
show two or more colours simultaneously in the projection map due to the overlap of ferroelectric 102
domains and domain walls along the light propagation path. 103
For the unpoled sample, the orientation map shows an irregular colour distribution on a very fine scale. 104
This is because the domain size of the as-grown PMN-PT is much smaller than the experimental 105
resolution (i.e., the wavelength of the light: 590 nm); therefore, the exact domain pattern may not be 106
clearly revealed. Compared to classical ferroelectrics (e.g., BaTiO
3
), the relatively small domain size in 107
relaxor ferroelectrics (on the order of several tens of nanometres before poling
18,19,20
) is attributed to 108
the presence of random fields/bonds that inhibits the growth of ferroelectric domains
21,22,23,24
. 109
After DC-poling, the regions with the same colour increase in size, and cross-like boundaries are 110
approximately along the [100] and [010] directions, which are associated with the projections of 71
o
111
4
domain walls [(101), (101
), (011) or (011
) planes] on the (001) plane. In this image, the colours of 112
most regions are neither red nor blue. Of particular importance is the significantly enlarged domain size 113
in the AC-poled sample where the in-plane size of the rhombohedral domain is on the millimetre scale. 114
It should be noted that the domain size obtained from phase-field simulation is much smaller than that 115
from experiments. This is due to the fact that the spatial scale in the phase-field simulation (512 nm) is 116
much smaller than that of the materials in experiments (millimeter scale). By increasing the scale in 117
phase-field simulation, the domain size of AC-poled crystal is found to increase (Extended Data Fig. 3). 118
It is difficult to perform a phase-field simulation on millimeter scale and at the same time to revolve the 119
polarization profiles across domain walls of the thickness of ~1 nm. In this work, we used phase-field 120
simulations to qualitatively analyse the domain evolution of PMN-28PT crystals during AC-poling. We 121
also characterized the cross-section domain structure of AC-poled and DC-poled samples to investigate 122
the domain size for the out-of-plane direction. As shown in Extended Data Fig. 4, we found that the 123
width between two neighbouring 109
o
domain walls is similar for both samples (~ 1 micron), indicating 124
that most 109
o
domain walls survived after AC-poling, which is consistent with phase-field simulations. 125
X-ray diffraction patterns confirm the main observations from the BIM images. Fig. 2b shows the {222} 126
reflections for the [001]-oriented PMN-28PT crystals. In this measurement, if the rhombohedral 127
domain variants are evenly distributed in the sample, there should be two diffraction peaks in the 2θ-ω 128
map: one peak is associated with the (222) plane at a lower 2θ, and the other peak is associated with the 129
remaining three {222} planes at a higher 2θ. Thus, the integrated intensity of the high-2θ reflection is 130
supposed to be three times that of the low-2θ reflection. This is approximately what has been observed 131
in the unpoled sample. The diffuse distribution of the diffraction along the ω axis is associated with the 132
lattice distortions due to the existence of domain walls. After DC-poling, the diffraction peaks converge 133
into distinctive sharper reflections, indicating that the domains become larger and the volume fraction 134
of domain walls is decreased. Eventually, in the AC-poled sample, only the high-2θ diffraction peak is 135
observed, and the diffusiveness of the diffraction peak along the ω axis is much smaller than that of the 136
DC-poled and unpoled samples (Extended Data Fig. 5). These features reveal that the X-ray beam is 137
almost incident on a single domain of AC-poled sample. The size of the beam here is approximately 1 138
mm
2
, which leads us to believe that the in-plane domain size of the AC-poled sample is equal to or 139
greater than this value. 140
Due to the unique domain structure, AC-poled PMN-28PT crystals exhibit numerous attractive 141
properties in addition to their ultrahigh piezoelectricity, including a high electro-optical coefficient γ
33
142
of 220 pm V
-1
, near-perfect light transmittance, and an enhanced birefringence (Extended Data Table 1). 143
Fig. 3a shows photos of the AC-poled and DC-poled samples, where AC-poled samples are clearly 144
transparent. The light transmittance of AC-poled sample is found to be very close to its theoretical limit 145
and is much higher than that of the DC-poled sample, especially for the visible light spectrum, as 146
shown in Fig. 3b. The light with a wavelength below 400 nm is completely absorbed due to the optical 147
absorption edge (~3.10 eV), which is similar to most oxygen-octahedral perovskites
25,26
. At a 148
wavelength above 400 nm, the light absorption coefficient of the AC-poled sample is found to be 149