# List of piezoelectric materials

This page lists properties of several commonly used piezoelectric materials.
Piezoelectric materials (PMs) can be broadly classified as either crystalline, ceramic, or polymeric. The most commonly produced piezoelectric ceramics are lead zirconate titanate (PZT), barium titanate, and lead titanate. Gallium nitride and zinc oxide can also be regarded as a ceramic due to their relatively wide band gaps. Semiconducting PMs offer features such as compatibility with integrated circuits and semiconductor devices. Inorganic ceramic PMs offer advantages over single crystals, including ease of fabrication into a variety of shapes and sizes not constrained crystallographic directions. Organic polymer PMs, such as PVDF, have low Young's modulus compared to inorganic PMs. Piezoelectric polymers (PVDF, 240 mV-m/N) possess higher piezoelectric stress constants (g$_{33}$), an important parameter in sensors, than ceramics (PZT, 11 mV-m/N), which show that they can be better sensors than ceramics. Moreover, piezoelectric polymeric sensors and actuators, due to their processing flexibility, can be readily manufactured into large areas, and cut into a variety of shapes. In addition polymers also exhibit high strength, high impact resistance, low dielectric constant, low elastic stiffness, and low density, thereby a high voltage sensitivity which is a desirable characteristic along with low acoustic and mechanical impedance useful for medical and underwater applications.
Among PMs, PZT ceramics are popular as they have a high sensitivity, a high g$_{33}$ value. They are however brittle. Furthermore, they show low Curie temperature, leading to constraints in terms of applications in harsh environmental conditions. However, promising is the integration of ceramic disks into industrial appliances moulded from plastic. This resulted in the development of PZT-polymer composites, and the feasible integration of functional PM composites on large scale, by simple thermal welding or by conforming processes. Several approaches towards lead-free ceramic PM have been reported, such as piezoelectric single crystals (langasite), and ferroelectric ceramics with a perovskite structure and bismuth layer-structured ferroelectrics (BLSF), which have been extensively researched. Also, several ferroelectrics with perovskite-structure (BaTiO$_3$ [BT], (Bi$_{1/2}$Na$_{1/2}$) TiO$_3$ [BNT], (Bi$_{1/2}$K$_{1/2}$) TiO$_3$ [BKT], KNbO$_3$ [KN], (K, Na) NbO$_3$ [KNN]) have been investigated for their piezoelectric properties.

## Key piezoelectric properties

The following table lists the following properties for piezoelectric materials
* The piezoelectric coefficients (d$_{33}$, d$_{31}$, d$_{15}$ etc.) measure the strain induced by an applied voltage (expressed as meters per volt). High d$_{ij}$ coefficients indicate larger displacements which are needed for motoring transducer devices. The coefficient d$_{33}$ measures deformation in the same direction (polarization axis) as the induced potential, whereas d$_{31}$ describes the response when the force is applied perpendicular to the polarization axis. The d$_{15}$ coefficient measures the response when the applied mechanical stress is due to shear deformation.
* Relative permittivity (ε$_r$) is the ratio between the absolute permittivity of the piezoelectric material, ε, and the vacuum permittivity, ε$_{0.}$
* The electromechanical coupling factor k is an indicator of the effectiveness with which a piezoelectric material converts electrical energy into mechanical energy, or converts mechanical energy into electrical energy. The first subscript to k denotes the direction along which the electrodes are applied; the second denotes the direction along which the mechanical energy is applied, or developed.
* The mechanical quality factor Q$_m$ is an important high-power property of piezoelectric ceramics. It is the inverse of the mechanical loss tan Φ.

## Table

Single crystals :
| Reference | Material & heterostructure used for the characterization (electrodes/material, electrode/substrate) | Orientation | Piezoelectric coefficients, d (pC/N) | Relative permittivity, ε$_r$ | Electromechanical coupling factor, k | Quality factor |
| Hutson 1963 | AlN | | d$_{15}$ = -4.07per | ε$_{33}$ = 11.4 | | |
| Hutson 1963 | AlN | | d$_{31}$ = -2 | | | |
| Hutson 1963 | AlN | | d$_{33}$ = 5 | | | |
| Cook et al. 1963 | BaTiO$_3$ | | d$_{15}$ = 392 | ε$_{11}$ = 2920 | k$_{15}$ = 0.57 | |
| Cook et al. 1963 | BaTiO$_3$ | | d$_{31}$ = -34.5 | ε$_{33}$ = 168 | k$_{31}$ = 0.315 | |
| Cook et al. 1963 | BaTiO$_3$ | | d$_{33}$ = 85.6 | | k$_{33}$ = 0.56 | |
| Warner et al. 1967 | LiNbO$_3$ (Au-Au) | <001> | d$_{15}$ = 68 | ε$_{11}$ = 84 | | |
| Warner et al. 1967 | LiNbO$_3$ (Au-Au) | <001> | d$_{22}$ = 21 | ε$_{33}$ = 30 | | |
| Warner et al. 1967 | LiNbO$_3$ (Au-Au) | <001> | d$_{31}$ = -1 | | k$_{31}$ = 0.02 | |
| Warner et al. 1967 | LiNbO$_3$ (Au-Au) | <001> | d$_{33}$ = 6 | | k$_t$ = 0.17 | |
| Smith et al. 1971 | LiNbO$_3$ | <001> | d$_{15}$ = 69.2 | ε$_{11}$ = 85.2 | | |
| Smith et al. 1971 | LiNbO$_3$ | <001> | d$_{22}$ = 20.8 | ε$_{33}$ = 28.2 | | |
| Smith et al. 1971 | LiNbO$_3$ | <001> | d$_{31}$ = -0.85 | | | |
| Smith et al. 1971 | LiNbO$_3$ | <001> | d$_{33}$ = 6 | | | |
| Yamada et al. 1967 | LiNbO$_3$ (Au-Au) | <001> | d$_{15}$ = 74 | ε$_{11}$ = 84.6 | | |
| Yamada et al. 1967 | LiNbO$_3$ (Au-Au) | <001> | d$_{22}$ = 21 | ε$_{33}$ = 28.6 | k$_{22}$ = 0.32 | |
| Yamada et al. 1967 | LiNbO$_3$ (Au-Au) | <001> | d$_{31}$ = -0.87 | | k$_{31}$ = 0.023 | |
| Yamada et al. 1967 | LiNbO$_3$ (Au-Au) | <001> | d$_{33}$ = 16 | | k$_{33}$ = 0.47 | |
| Yamada et al. 1969 | LiTaO$_3$ | | d$_{15}$ = 26 | ε$_{11}$ = 53 | | |
| Yamada et al. 1969 | LiTaO$_3$ | | d$_{22}$ = 8.5 | ε$_{33}$ = 44 | | |
| Yamada et al. 1969 | LiTaO$_3$ | | d$_{31}$ = -3 | | | |
| Yamada et al. 1969 | LiTaO$_3$ | | d$_{33}$ = 9.2 | | | |
| Cao et al. 2002 | PMN-PT (33%) | | d$_{15}$ = 146 | ε$_{11}$ = 1660 | k$_{15}$ = 0.32 | |
| Cao et al. 2002 | PMN-PT (33%) | | d$_{31}$ = -1330 | ε$_{33}$ = 8200 | k$_{31}$ = 0.59 | |
| Cao et al. 2002 | PMN-PT (33%) | | d$_{33}$ = 2820 | | k$_{33}$ = 0.94 | |
| Cao et al. 2002 | PMN-PT (33%) | | | | k$_t$ = 0.64 | |
| Badel et al. 2006 | PMN-25PT | <110> | d$_{31}$ = -643 | ε$_{33}$ = 2560 | k$_{31}$ = -0.73 | 362 |
| Kobiakov 1980 | ZnO | | d$_{15}$ = -8.3 | ε$_{11}$ = 8.67 | k$_{15}$ = 0.199 | |
| Kobiakov 1980 | ZnO | | d$_{31}$ = -5.12 | ε$_{33}$ = 11.26 | k$_{31}$ = 0.181 | |
| Kobiakov 1980 | ZnO | | d$_{33}$ = 12.3 | | k$_{33}$ = 0.466 | |
| Zgonik et al. 1994 | ZnO (pure with lithium dopant) | | d$_{15}$ = -13.3 | | k$_r$ = 8.2 | |
| Zgonik et al. 1994 | ZnO (pure with lithium dopant) | | d$_{31}$ = -4.67 | | | |
| Zgonik et al. 1994 | ZnO (pure with lithium dopant) | | d$_{33}$ = 12.0 | | | |
| Zgonik et al. 1994 | BaTiO$_3$ single crystals | [001] (single domain) | d$_{33}$ = 90 | | | |
| Zgonik et al. 1994 | BaTiO$_3$ single crystals | [111] (single domain) | d$_{33}$ = 224 | | | |
| Zgonik et al. 1994 | BaTiO$_3$ single crystals | [111] neutral (domain size of 100 ľm) | d$_{33}$ = 235 | ε$_{33}$ = 1984 | k$_{33}$ = 54.4 | |
| Zgonik et al. 1994 | BaTiO$_3$ single crystals | [111] neutral (domain size of 60 ľm) | d$_{33}$ = 241 | ε$_{33}$ = 1959 | k$_{33}$ = 55.9 | |
| Zgonik et al. 1994 | BaTiO$_3$ single crystals | [111] (domain size of 22 ľm) | d$_{33}$ = 256 | ε$_{33}$ = 2008 | k$_{33}$ = 64.7 | |
| Zgonik et al. 1994 | BaTiO$_3$ single crystals | [111] neutral (domain size of 15 ľm) | d$_{33}$ = 274 | ε$_{33}$ = 2853 | k$_{33}$ = 66.1 | |
| Zgonik et al. 1994 | BaTiO$_3$ single crystals | [111] neutral (domain size of 14 ľm) | d$_{33}$ = 289 | ε$_{33}$ = 1962 | k$_{33}$ = 66.7 | |
| Zgonik et al. 1994 | BaTiO$_3$ single crystals | [111] neutral | d$_{33}$ = 331 | ε$_{33}$ = 2679 | k$_{33}$ = 65.2 | |
| | LN crystal | | d$_{31}$ = -4.5 d$_{33}$ = -0.27 | | | |
| Li et al. 2010 | PMNT31 | | d$_{33}$ = 2000 | ε$_{33}$ = 5100 | k$_{31}$ = 80 | |
| Li et al. 2010 | PMNT31 | | d$_{31}$ = -750 | | | |
| Zhang et al. 2002 | PMNT31-A | | 1400 | ε$_{33}$ = 3600 | | |
| Zhang et al. 2002 | PMNT31-B | | 1500 | ε$_{33}$ = 4800 | | |
| Zhang et al. 2002 | PZNT4.5 | | d$_{33}$ = 2100 | ε$_{33}$ = 4400 | k$_{31}$ = 83 | |
| Zhang et al. 2002 | PZNT4.5 | | d$_{31}$ = -900 | | | |
| Zhang et al. 2004 | PZNT8 | | d$_{33}$ = 2500 | ε$_{33}$ = 6000 | k$_{31}$ = 89 | |
| Zhang et al. 2004 | PZNT8 | | d$_{31}$ = -1300 | | | |
| Zhang et al. 2004 | PZNT12 | | d$_{33}$ = 576 | ε$_{33}$ = 870 | k$_{31}$ = 52 | |
| Zhang et al. 2004 | PZNT12 | | d$_{31}$ = -217 | | | |
| Yamashita et al. 1997 | PSNT33 | | | ε$_{33}$ = 960 | / | |
| Yasuda et al. 2001 | PINT28 | | 700 | ε$_{33}$ = 1500 | / | |
| Guo et al. 2003 | PINT34 | | 2000 | ε$_{33}$ = 5000 | / | |
| Hosono et al. 2003 | PIMNT | | 1950 | ε$_{33}$ = 3630 | / | |
| Zhang et al. 2002 | PYNT40 | | d$_{33}$ = 1200 | ε$_{33}$ = 2700 | k$_{31}$ = 76 | |
| Zhang et al. 2002 | PYNT40 | | d$_{31}$ = -500 | | | |
| Zhang et al. 2012 | PYNT45 | | d$_{33}$ = 2000 | ε$_{33}$ = 2000 | k$_{31}$ = 78 | |
| Zhang et al. 2003 | BSPT57 | | d$_{33}$ = 1200 | ε$_{33}$ = 3000 | k$_{31}$ = 77 | |
| Zhang et al. 2003 | BSPT57 | | d$_{31}$ = -560 | | | |
| Zhang et al. 2003 | BSPT58 | | d$_{33}$ = 1400 | ε$_{33}$ = 3200 | k$_{31}$ = 80 | |
| Zhang et al. 2003 | BSPT58 | | d$_{31}$ = -670 | | | |
| Zhang et al. 2004 | BSPT66 | | d$_{33}$ = 440 | ε$_{33}$ = 820 | k$_{31}$ = 52 | |
| Zhang et al. 2004 | BSPT66 | | d$_{31}$ = -162 | | | |
| Ye et al. 2008 | BSPT57 | | d$_{33}$ = 1150 d$_{31}$ = -520 | ε$_{33}$ = 3000 | k$_{31}$ = 0.52 k$_{33}$ = 0.91 | |
| Ye et al. 2008 | BSPT66 | | d$_{33}$ = 440 | ε$_{33}$ = 820 | k$_{31}$ = 0.52 k$_{33}$ = 0.88 | |
| Ye et al. 2008 | BSPT66 | | d$_{31}$ = -162 | | | |
| Ye et al. 2008 | PZNT4.5 | | d$_{33}$ = 2000 d$_{31}$ = -970 | ε$_{33}$ = 5200 | k$_{31}$ = 0.50 k$_{33}$ = 0.91 | |
| Ye et al. 2008 | PZNT8 | | d$_{31}$ = -1455 | ε$_{33}$ = 7700 | k$_{31}$ = 0.60 k$_{33}$ = 0.94 | |
| Ye et al. 2008 | PZNT12 | | d$_{33}$ = 576 d$_{31}$ = -217 | ε$_{33}$ = 870 | k$_{31}$ = 0.52 k$_{33}$ = 0.86 | |
| Ye et al. 2008 | PMNT33 | | d$_{33}$ = 2820 d$_{31}$ = -1330 | ε$_{33}$ = 8200 | k$_{31}$ = 0.59 k$_{33}$ = 0.94 | |
| Matsubara et al. 2004 | KCN-modified KNN | | d$_{33}$ = 100 d$_{31}$ = -180 | ε$_{33}$ = 220-330 | k$_p$ = 33-39 | 1200 |
| Ryu et al. 2007 | KZT modifiedKNN | | d$_{33}$ = 126 | ε$_{33}$ = 590 | k$_p$ = 42 | 58 |
| Matsubara et al. 2005 | KCT modified KNN | | d$_{33}$ = 190 | ε$_{33}$ = | k$_p$ = 42 | 1300 |
| Wang et al. 2007 | Bi$_2$O$_3$ doped KNN | | d$_{33}$ = 127 | ε$_{33}$ = 1309 | k$_p$ = 28.3 | |
| Jiang et al. 2009 | doped KNN-0.005BF | | d$_{33}$ = 257 | ε$_{33}$ = 361 | k$_p$= 52 | 45 |
Ceramics :
| Reference | Material & heterostructure used for the characterization (electrodes/material, electrode/substrate) | Orientation | Piezoelectric coefficients, d (pC/N) | Relative permittivity, ε$_r$ | Electromechanical coupling factor, k | Quality factor |
| Berlincourt et al. 1958 | BaTiO$_3$ | | d$_{15}$ = 270 | ε$_{11}$ = 1440 | k$_{15}$ = 0.57 | |
| Berlincourt et al. 1958 | BaTiO$_3$ | | d$_{31}$ = -79 | ε$_{33}$ = 1680 | k$_{31}$ = 0.49 | |
| Berlincourt et al. 1958 | BaTiO$_3$ | | d$_{33}$ = 191 | | k$_{33}$ = 0.47 | |
| Tang et al. 2011 | BFO | | d$_{33}$ = 37 | | k$_t$ = 0.6 | |
| Zhang et al. 1999 | PMN-PT | | d$_{31}$ = -74 | ε$_{33}$ = 1170 | k$_{31}$ = -0.312 | 283 |
| | PZT-5A | | d$_{31}$ = -171 | ε$_{33}$ = 1700 | k$_{31}$ = 0.34 | |
| | PZT-5A | | d$_{33}$ = 374 | | k$_{33}$ = 0.7 | |
| | PZT-5H | | d$_{15}$ = 741 | ε$_{11}$ = 3130 | k$_{15}$ = 0.68 | 65 |
| | PZT-5H | | d$_{31}$ = -274 | ε$_{33}$ = 3400 | k$_{31}$ = 0.39 | |
| | PZT-5H | | d$_{33}$ = 593 | | k$_{33}$ = 0.75 | |
| | PZT-5K | | d$_{33}$ = 870 | ε$_{33}$ = 6200 | k$_{33}$ = 0.75 | |
| Tanaka et al. 2009 | PZN7%PT | | d$_{33}$ = 2400 | ε$_r$ = 6500 | k$_{33}$ = 0.94 k$_t$ = 0.55 | |
| Pang et al. 2010 | ANSZ | | d$_{33}$ = 295 | 1.61 | 45.5 | 84 |
| Park et al. 2006 | KNN-BZ | | d$_{33}$ = 400 | 2 | 57.4 | 48 |
| Cho et al. 2007 | KNN-BT | | d$_{33}$ = 225 | 1.06 | 36.0 | |
| Park et al. 2007 | KNN-ST | | d$_{33}$ = 220 | 1.45 | 40.0 | 70 |
| Zhao et al. 2007 | KNN-CT | | d$_{33}$ = 241 | 1.32 | 41.0 | |
| Zhang et al. 2006 | LNKN | | d$_{33}$ = 314 | ~700 | 41.2 | |
| Saito et al. 2004 | KNN-LS | | d$_{33}$ = 270 | 1.38 | 50.0 | |
| Saito et al. 2004 | LF4 | | d$_{33}$ = 300 | 1.57 | | |
| Tanaka et al. 2009 | Oriented LF4 | | d$_{33}$ = 416 | 1.57 | 61.0 | |
| Pang et al. 2010 | ANSZ | | d$_{33}$ = 295 | 1.61 | 45.5 | 84 |
| Park et al. 2006 | KNN-BZ | | d$_{33}$ = 400 | 2 | 57.4 | 48 |
| Cho et al. 2007 | KNN-BT | | d$_{33}$ = 225 | 1.06 | 36.0 | |
| Park et al. 2007 | KNN-ST | | d$_{33}$ = 220 | 1.45 | 40.0 | 70 |
| Maurya et al. 2013 | KNN-CT | | d$_{33}$ = 241 | 1.32 | 41.0 | |
| Maurya et al. 2013 | NBT-BT | (001) Textured samples | d$_{33}$ = 322 | | ... | |
| Gao et al. 2008 | NBT-BT-KBT | (001) Textured samples | d$_{33}$ = 192 | | | |
| Zou et al. 2016 | NBT-KBT | (001) Textured samples | d$_{33}$ = 134 | | k$_p$= 35 | |
| Saito et al. 2004 | NBT-KBT | (001) Textured samples | d$_{33}$ = 217 | | k$_p$ = 61 | |
| Chang et al. 2009 | KNLNTS | (001) Textured samples | d$_{33}$ = 416 | | k$_p$ = 64 | |
| Chang et al. 2011 | KNNS | (001) Textured samples | d$_{33}$ = 208 | | k$_p$ = 63 | |
| Hussain et al. 2013 | KNLN | (001) Textured samples | d$_{33}$ = 192 | | k$_p$ = 60 | |
| Takao et al. 2006 | KNNT | (001) Textured samples | d$_{33}$ = 390 | | k$_p$ = 54 | |
| Li et al. 2012 | KNN 1 CuO | (001) Textured samples | d$_{33}$ = 123 | | k$_p$ = 54 | |
| Cho et al. 2012 | KNN-CuO | (001) Textured samples | d$_{33}$ = 133 | | k$_p$ = 46 | |
| Hao et al. 2012 | NKLNT | (001) Textured samples | d$_{33}$ = 310 | | k$_p$ = 43 | |
| Gupta et al. 2014 | KNLN | (001) Textured samples | d$_{33}$ = 254 | | | |
| Hao et al. 2012 | KNN | (001) Textured samples | d$_{33}$ = 180 | | k$_p$ = 44 | |
| Bai et al. 2016 | BCZT | (001) Textured samples | d$_{33}$ = 470 | | k$_p$ = 47 | |
| Ye et al. 2013 | BCZT | (001) Textured samples | d$_{33}$ = 462 | | k$_p$ = 49 | |
| Schultheiß et al. 2017 | BCZT-T-H | (001) Textured samples | d$_{33}$ = 580 | | | |
| OMORI et al. 1990 | BCT | (001) Textured samples | d$_{33}$ = 170 | | | |
| Chan et al. 2008 | Pz34 (doped PbTiO$_3$) | | d$_{15}$ = 43.3 | ε$_{33}$ = 237 | k$_{31}$ = 4.6 | 700 |
| Chan et al. 2008 | Pz34 (doped PbTiO$_3$) | | d$_{31}$ = -5.1 | ε$_{33}$ = 208 | k$_{33}$ = 39.6 | |
| Chan et al. 2008 | Pz34 (doped PbTiO$_3$) | | d$_{33}$ = 46 | | k$_{15}$ = 22.8 | |
| Chan et al. 2008 | Pz34 (doped PbTiO$_3$) | | | | k$_p$ = 7.4 | |
| Lee et al. 2009 | BNKLBT | | d$_{33}$ = 163 | ε$_r$ = 766 | k$_{31}$ = 0.188 | 142 |
| Lee et al. 2009 | BNKLBT | | | ε$_{33}$ = 444.3 | k$_t$ = 0.524 | |
| Lee et al. 2009 | BNKLBT | | | | k$_p$ = 0.328 | |
| Sasaki et al. 1999 | KNLNTS | | | ε$_r$ = 1156 | k$_{31}$ = 0.26 | 80 |
| Sasaki et al. 1999 | KNLNTS | | | ε$_{33}$ = 746 | k$_t$ = 0.32 | |
| Sasaki et al. 1999 | KNLNTS | | | | k$_p$ = 0.43 | |
| Takenaka et al. 1991 | (Bi$_{0.5}$Na$_{0.5}$)TiO$_3$ (BNT)-based BNKT | | d$_{31}$ = 46 | ε$_r$ = 650 | k$_p$ = 0.27 | |
| Takenaka et al. 1991 | (Bi$_{0.5}$Na$_{0.5}$)TiO$_3$ (BNT)-based BNKT | | d$_{33}$ = 150 | | k$_{31}$ = 0.165 | |
| Tanaka et al. 1960 | (Bi$_{0.5}$Na$_{0.5}$)TiO$_3$ (BNT)-based BNBT | | d$_{31}$ = 40 | ε$_r$ = 580 | k$_{31}$ = 0.19 | |
| Tanaka et al. 1960 | (Bi$_{0.5}$Na$_{0.5}$)TiO$_3$ (BNT)-based BNBT | | d$_{33}$ = 12.5 | | k$_{33}$ = 0.55 | |
| Hutson 1960 | CdS | | d$_{15}$ = -14.35 | | | |
| Hutson 1960 | CdS | | d$_{31}$ = -3.67 | | | |
| Hutson 1960 | CdS | | d$_{33}$ = 10.65 | | | |
| Schofield et al. 1957 | CdS | | d$_{31}$ = -1.53 | | | |
| Schofield et al. 1957 | CdS | | d$_{33}$ = 2.56 | | | |
| Egerton et al. 1959 | BaCaOTi | | d$_{31}$ = -50 | | k$_{15}$ = 0.19 | 400 |
| Egerton et al. 1959 | BaCaOTi | | d$_{33}$ = 150 | | k$_{31}$ = 0.49 | |
| Egerton et al. 1959 | BaCaOTi | | | | k$_{33}$ = 0.325 | |
| Ikeda et al. 1961 | Nb$_2$O$_6$Pb | | d$_{31}$ = -11 | | k$_r$ = 0.07 | 11 |
| Ikeda et al. 1961 | Nb$_2$O$_6$Pb | | d$_{33}$ = 80 | | k$_{31}$ = 0.045 | |
| Ikeda et al. 1961 | Nb$_2$O$_6$Pb | | | | k$_{33}$ = 0.042 | |
| Ikeda et al. 1962 | C$_6$H$_{17}$N$_3$O$_{10}$S | | d$_{23}$ = 84 | | k$_{21}$ = 0.18 | |
| Ikeda et al. 1962 | C$_6$H$_{17}$N$_3$O$_{10}$S | | d$_{21}$ = 22.7 | | k$_{22}$ = 0.18 | |
| Ikeda et al. 1962 | C$_6$H$_{17}$N$_3$O$_{10}$S | | d$_{25}$ = 22 | | k$_{23}$ = 0.44 | |
| Brown et al. 1962 | BaTiO$_3$ (95%) BaZrO$_3$ (5%) | | | | k$_{15}$ = 0.15 | 200 |
| Brown et al. 1962 | BaTiO$_3$ (95%) BaZrO$_3$ (5%) | | d$_{31}$ = -60 | | k$_{31}$ = 0.40 | |
| Brown et al. 1962 | BaTiO$_3$ (95%) BaZrO$_3$ (5%) | | d$_{33}$ = 150 | | k$_{33}$ = 0.28 | |
| Huston 1960 | BaNb$_2$O$_6$ (60%) Nb$_2$O$_6$Pb (40%) | | d$_{31}$ = -25 | | k$_r$ = 0.16 | |
| Baxter et al. 1960 | BaNb$_2$O$_6$ (50%) Nb$_2$O$_6$Pb (50%) | | d$_{31}$= -36 | | k$_r$ = 0.16 | |
| Pullin 1962 | BaTiO$_3$ (97%) CaTiO$_3$ (3%) | | d$_{31}$ = -53 | ε$_{33}$ = 1390 | k$_{15}$ = 0.39 | |
| Pullin 1962 | BaTiO$_3$ (97%) CaTiO$_3$ (3%) | | d$_{33}$ = 135 | | k$_{31}$ = 0.17 | |
| Pullin 1962 | BaTiO$_3$ (97%) CaTiO$_3$ (3%) | | | | k$_{33}$ = 0.43 | |
| Berlincourt et al. 1960 | BaTiO$_3$ (95%) CaTiO$_3$ (5%) | | d$_{15}$ = -257 | ε$_{33}$ = 1355 | k$_{15}$ = 0.495 | 500 |
| Berlincourt et al. 1960 | BaTiO$_3$ (95%) CaTiO$_3$ (5%) | | d$_{31}$ = -58 | | k$_{31}$ = 0.19 | |
| Berlincourt et al. 1960 | BaTiO$_3$ (95%) CaTiO$_3$ (5%) | | d$_{33}$ = 150 | | k$_{33}$ = 0.49 | |
| Berlincourt et al. 1960 | BaTiO$_3$ (95%) CaTiO$_3$ (5%) | | | | k$_r$ = 0.3 | |
| Berlincourt et al. 1960 | BaTiO$_3$ (96%) PbTiO$_3$ (4%) | | d$_{31}$ = -38 | ε$_{33}$ = 990 | k$_{15}$ = 0.34 | |
| Berlincourt et al. 1960 | BaTiO$_3$ (96%) PbTiO$_3$ (4%) | | d$_{33}$ = 105 | | k$_{31}$ = 0.14 | |
| Berlincourt et al. 1960 | BaTiO$_3$ (96%) PbTiO$_3$ (4%) | | | | k$_{33}$ = 0.39 | |
| Jaffe et al. 1955 | PbHfO$_3$ (50%) PbTiO$_3$ (50%) | | d$_{31}$ = -54 | | k$_r$ = 0.38 | |
| Kell 1962 | Nb$_2$O$_6$Pb (80%) BaNb$_2$O$_6$ (20%) | | d$_{31}$ = 25 | | k$_r$ = 0.20 | 15 |
| Brown et al. 1962 | Nb$_2$O$_6$Pb (70%) BaNb$_2$O$_6$ (30%) | | d$_{31}$ = -40 | ε$_{33}$ = 900 | k$_{31}$ = 0.13 | 350 |
| Brown et al. 1962 | Nb$_2$O$_6$Pb (70%) BaNb$_2$O$_6$ (30%) | | d$_{33}$ = 100 | | k$_{33}$ = 0.3 | |
| Brown et al. 1962 | Nb$_2$O$_6$Pb (70%) BaNb$_2$O$_6$ (30%) | | | | k$_r$ = 0.24 | |
| Berlincourt et al. 1960 | PbTiO$_3$ (52%) PbZrO3 (48%) | | d$_{15}$ = 166 | | k$_{15}$ = 0.40 | 1170 |
| Berlincourt et al. 1960 | PbTiO$_3$ (52%) PbZrO3 (48%) | | d$_{31}$ = -43 | | k$_{31}$ = 0.17 | |
| Berlincourt et al. 1960 | PbTiO$_3$ (52%) PbZrO3 (48%) | | d$_{33}$ = 110 | | k$_{33}$ = 0.43 | |
| Berlincourt et al. 1960 | PbTiO$_3$ (52%) PbZrO3 (48%) | | | | k$_r$ = 0.28 | |
| Berlincourt et al. 1960 | PbTiO$_3$ (50%) lead Zirconate (50%) | | d$_{15}$ = 166 | | k$_{15}$ = 0.504 | 950 |
| Berlincourt et al. 1960 | PbTiO$_3$ (50%) lead Zirconate (50%) | | d$_{31}$ = -43 | | k$_{31}$ = 0.23 | |
| Berlincourt et al. 1960 | PbTiO$_3$ (50%) lead Zirconate (50%) | | d$_{33}$ = 110 | | k$_{33}$ = 0.546 | |
| Berlincourt et al. 1960 | PbTiO$_3$ (50%) lead Zirconate (50%) | | | | k$_r$ = 0.397 | |
| Egerton et al. 1959 | KNbO$_3$ (50%) NaNbO$_3$ (50%) | | d$_{31}$ = -32 | | | 140 |
| Egerton et al. 1959 | KNbO$_3$ (50%) NaNbO$_3$ (50%) | | d$_{33}$ = 80 | | k$_{31}$ = 0.21 | |
| Egerton et al. 1959 | KNbO$_3$ (50%) NaNbO$_3$ (50%) | | | | k$_{33}$ = 0.51 | |
| Brown et al. 1962 | NaNbO$_3$ (80%) Cd$_2$Nb$_2$O$_7$ (20%) | | d$_{31}$ = -80 | ε$_{33}$ = 2000 | k$_{31}$ = 0.17 | |
| Brown et al. 1962 | NaNbO$_3$ (80%) Cd$_2$Nb$_2$O$_7$ (20%) | | d$_{33}$ = 200 | | k$_{33}$ = 0.42 | |
| Brown et al. 1962 | NaNbO$_3$ (80%) Cd$_2$Nb$_2$O$_7$ (20%) | | | | k$_r$ = 0.30 | |
| Schofield et al. 1957 | BaTiO$_3$ (95%) CaTiO$_3$ (5%) CoCO3 (0.25%) | | d$_{31}$ = -60 | ε$_{33}$ = 1605 | k$_r$ = 0.33 | |
| Pullin 1962 | BaTiO$_3$ (80%) PbTiO$_3$ (12%) CaTiO$_3$ (8%) | | d$_{31}$ = -31 | | k$_{31}$ = 0.15 | 1200 |
| Pullin 1962 | BaTiO$_3$ (80%) PbTiO$_3$ (12%) CaTiO$_3$ (8%) | | d$_{33}$ = 79 | | k$_{33}$ = 0.41 | |
| Pullin 1962 | BaTiO$_3$ (80%) PbTiO$_3$ (12%) CaTiO$_3$ (8%) | | | | k$_r$ = 0.24 | |
| Defaÿ 2011 | AlN (Pt-Mo) | | d$_{31}$ = -2.5 | | | |
| Shibata et al. 2011 | KNN(Pt-Pt) | <001> | d$_{31}$ = -96.3 | ε$_r$ = 1100 | | |
| Shibata et al. 2011 | KNN(Pt-Pt) | <001> | d$_{33}$ = 138.2 | | | |
| Sessler 1981 | PVDF | | d$_{31}$ = 17.9 | | k$_{31}$ = 10.3 | |
| Sessler 1981 | PVDF | | d$_{32}$ = 0.9 | | k$_{33}$ = 12.6 | |
| Sessler 1981 | PVDF | | d$_{33}$ = -27.1 | | | |
| Ren et al. 2017 | PVDF | | d$_{31}$ = 23 | ε$_r$ = 106 | | |
| Ren et al. 2017 | PVDF | | d$_{32}$ = 2 | | | |
| Ren et al. 2017 | PVDF | | d$_{33}$ = -21 | | | |
| Tsubouchi et al. 1981 | Epi AlN/Al$_2$O$_3$ | <001> | d$_{33}$ = 5.53 | ε$_{33}$ = 9.5 | k$_t$ = 6.5 | 2490 |
Nanomaterials :
| Reference | Material | Structure | Piezoelectric coefficients, d (pC/N) | Characterization method | Size (nm) |
| Ke et al. 2008 | NaNbO$_3$ | nanowire | d$_{33}$ = 0.85-4.26 pm/V | PFM | d = 100 |
| Wang et al. 2008 | KNbO$_3$ | nanowire | d$_{33}$ = 0.9 pm/V | PFM | d = 100 |
| Zhang et al. 2004 | PZT | nanowire | | PFM | d = 45 |
| Zhao et al. 2004 | ZnO | nanobelt | d$_{33}$ = 14.3-26.7 pm/V | PFM | w = 360 t = 65 |
| Luo et al. 2003 | PZT | nanoshell | d$_{33}$ = 90 pm/V | PFM | d = 700 t = 90 |
| Yun et al. 2002 | BaTiO3 | nanowire | d$_{33}$ = 0.5 pm/V | PFM | d = 120 |
| Lin et al. 2008 | CdS | nanowire | | Bending with AFM tip | d = 150 |
| Wang et al. 2007 | PZT | nanofiber | piezoelectric voltage constant~0.079 Vm/N | Bending using a tungsten probe | d = 10 |
| Wang et al. 2007 | BaTiO$_3$ | - | d$_{33}$ = 45 pC/N | Direct tensile test | d ~ 280 |
| Jeong et al. 2014 | Alkaline niobate (KNLN) | film | d$_{33}$ = 310 pC/N | - | |
| Park et al. 2010 | BaTiO$_3$ | Thin film | d$_{33}$ = 190 pC/N | | |
| Stoppel et al. 2011 | AlN | Thin film | d$_{33}$ =5 pC/N | AFM | |
| Lee et al. 2017 | WSe2 | 2D nanosheet | d$_{11}$ = 3.26 pm/V | | |
| Zhu et al. 2014 | MoS2 | Free standing layer | e$_{11}$ = 2900pc/m | AFM | |
| Zhong et al. 2017 | PET/EVA/PET | film | d$_{33}$ = 6300 pC/N | | |