Chemistry:List of piezoelectric materials

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This page lists properties of several commonly used piezoelectric materials.

Piezoelectric materials (PMs) can be broadly classified as either crystalline, ceramic, or polymeric.[1] 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 (g33), 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 g33 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 (BaTiO3 [BT], (Bi1/2Na1/2) TiO3 [BNT], (Bi1/2K1/2) TiO3 [BKT], KNbO3 [KN], (K, Na) NbO3 [KNN]) have been investigated for their piezoelectric properties.

Key piezoelectric properties

The following table lists the following properties for piezoelectric materials

  • The piezoelectric coefficients (d33, d31, d15 etc.) measure the strain induced by an applied voltage (expressed as meters per volt). High dij coefficients indicate larger displacements which are needed for motoring transducer devices. The coefficient d33 measures deformation in the same direction (polarization axis) as the induced potential, whereas d31 describes the response when the force is applied perpendicular to the polarization axis. The d15 coefficient measures the response when the applied mechanical stress is due to shear deformation.
  • Relative permittivity (εr) is the ratio between the absolute permittivity of the piezoelectric material, ε, and the vacuum permittivity, ε0.
  • 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 Qm 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, εr Electromechanical coupling factor, k Quality factor
Hutson 1963[2] AlN d15 = -4.07per ε33 = 11.4
d31 = -2
d33 = 5
Cook et al. 1963[3] BaTiO3 d15 = 392 ε11 = 2920 k15 = 0.57
d31 = -34.5 ε33 = 168 k31 = 0.315
d33 = 85.6 k33 = 0.56
Warner et al. 1967[4] LiNbO3 (Au-Au) <001> d15 = 68 ε11 = 84
d22 = 21 ε33 = 30
d31 = -1 k31 = 0.02
d33 = 6 kt = 0.17
Smith et al. 1971[5] LiNbO3 <001> d15 = 69.2 ε11 = 85.2
d22 = 20.8 ε33 = 28.2
d31 = -0.85
d33 = 6
Yamada et al. 1967[6] LiNbO3 (Au-Au) <001> d15 = 74 ε11 = 84.6
d22 = 21 ε33 = 28.6 k22 = 0.32
d31 = -0.87 k31 = 0.023
d33 = 16 k33 = 0.47
Yamada et al. 1969[7] LiTaO3 d15 = 26 ε11 = 53
d22 = 8.5 ε33 = 44
d31 = -3
d33 = 9.2
Cao et al. 2002[8] PMN-PT (33%) d15 = 146 ε11 = 1660 k15 = 0.32
d31 = -1330 ε33 = 8200 k31 = 0.59
d33 = 2820 k33 = 0.94
kt = 0.64
Badel et al. 2006[9] PMN-25PT <110> d31 = -643 ε33 = 2560 k31 = -0.73 362
Kobiakov 1980[10] ZnO d15 = -8.3 ε11 = 8.67 k15 = 0.199
d31 = -5.12 ε33 = 11.26 k31 = 0.181
d33 = 12.3 k33 = 0.466
Zgonik et al. 1994[11] ZnO (pure with lithium dopant) d15 = -13.3 kr = 8.2
d31 = -4.67
d33 = 12.0
Zgonik et al. 1994[12] BaTiO3 single crystals [001] (single domain) d33 = 90
Zgonik et al. 1994[12] BaTiO3 single crystals [111] (single domain) d33 = 224
Zgonik et al. 1994[12] BaTiO3 single crystals [111] neutral (domain size of 100 ľm) d33 = 235 ε33 = 1984 k33 = 54.4
Zgonik et al. 1994[12] BaTiO3 single crystals [111] neutral (domain size of 60 ľm) d33 = 241 ε33 = 1959 k33 = 55.9
Zgonik et al. 1994[12] BaTiO3 single crystals [111] (domain size of 22 ľm) d33 = 256 ε33 = 2008 k33 = 64.7
Zgonik et al. 1994[12] BaTiO3 single crystals [111] neutral (domain size of 15 ľm) d33 = 274 ε33 = 2853 k33 = 66.1
Zgonik et al. 1994[12] BaTiO3 single crystals [111] neutral (domain size of 14 ľm) d33 = 289 ε33 = 1962 k33 = 66.7
Zgonik et al. 1994[12] BaTiO3 single crystals [111] neutral d33 = 331 ε33 = 2679 k33 = 65.2
[13] LN crystal d31 = -4.5

d33 = -0.27

Li et al. 2010[14] PMNT31 d33 = 2000 ε33 = 5100 k31 = 80
d31 = -750
Zhang et al. 2002[15] PMNT31-A 1400 ε33 = 3600
Zhang et al. 2002[15] PMNT31-B 1500 ε33 = 4800
Zhang et al. 2002[15] PZNT4.5 d33 = 2100 ε33 = 4400 k31 = 83
d31 = -900
Zhang et al. 2004[16] PZNT8 d33 = 2500 ε33 = 6000 k31 = 89
d31 = -1300
Zhang et al. 2004[16] PZNT12 d33 = 576 ε33 = 870 k31 = 52
d31 = -217
Yamashita et al. 1997[17] PSNT33 ε33 = 960 /
Yasuda et al. 2001[18] PINT28 700 ε33 = 1500 /
Guo et al. 2003[19] PINT34 2000 ε33 = 5000 /
Hosono et al. 2003[20] PIMNT 1950 ε33 = 3630 /
Zhang et al. 2002[15] PYNT40 d33 = 1200 ε33 = 2700 k31 = 76
d31 = -500
Zhang et al. 2012[21] PYNT45 d33 = 2000 ε33 = 2000 k31 = 78
Zhang et al. 2003[22] BSPT57 d33 = 1200 ε33 = 3000 k31 = 77
d31 = -560
Zhang et al. 2003[23] BSPT58 d33 = 1400 ε33 = 3200 k31 = 80
d31 = -670
Zhang et al. 2004[16] BSPT66 d33 = 440 ε33 = 820 k31 = 52
d31 = -162
Ye et al. 2008[24] BSPT57 d33 = 1150

d31 = -520

ε33 = 3000 k31 = 0.52

k33 = 0.91

Ye et al. 2008[24] BSPT66 d33 = 440 ε33 = 820 k31 = 0.52

k33 = 0.88

d31 = -162
Ye et al. 2008[24] PZNT4.5 d33 = 2000

d31 = -970

ε33 = 5200 k31 = 0.50

k33 = 0.91

Ye et al. 2008[24] PZNT8 d31 = -1455 ε33 = 7700 k31 = 0.60

k33 = 0.94

Ye et al. 2008[24] PZNT12 d33 = 576

d31 = -217

ε33 = 870 k31 = 0.52

k33 = 0.86

Ye et al. 2008[24] PMNT33 d33 = 2820

d31 = -1330

ε33 = 8200 k31 = 0.59

k33 = 0.94

Matsubara et al. 2004[25] KCN-modified KNN d33 = 100

d31 = -180

ε33 = 220-330 kp = 33-39 1200
Ryu et al. 2007[26] KZT modifiedKNN d33 = 126 ε33 = 590 kp = 42 58
Matsubara et al. 2005[27] KCT modified KNN d33 = 190 ε33 = kp = 42 1300
Wang et al. 2007[28] Bi2O3 doped KNN d33 = 127 ε33 = 1309 kp = 28.3
Jiang et al. 2009[29] doped KNN-0.005BF d33 = 257 ε33 = 361 kp= 52 45
Ceramics
Reference Material & heterostructure used for the characterization (electrodes/material, electrode/substrate) Orientation Piezoelectric coefficients, d (pC/N) Relative permittivity, εr Electromechanical coupling factor, k Quality factor
Berlincourt et al. 1958[30] BaTiO3 d15 = 270 ε11 = 1440 k15 = 0.57
d31 = -79 ε33 = 1680 k31 = 0.49
d33 = 191 k33 = 0.47
Tang et al. 2011[31] BFO d33 = 37 kt = 0.6
Zhang et al. 1999[32] PMN-PT d31 = -74 ε33 = 1170 k31 = -0.312 283
[33] PZT-5A d31 = -171 ε33 = 1700 k31 = 0.34
d33 = 374 k33 = 0.7
[34] PZT-5H d15 = 741 ε11 = 3130 k15 = 0.68 65
d31 = -274 ε33 = 3400 k31 = 0.39
d33 = 593 k33 = 0.75
[35] PZT-5K d33 = 870 ε33 = 6200 k33 = 0.75
Tanaka et al. 2009[36] PZN7%PT d33 = 2400 εr = 6500 k33 = 0.94

kt = 0.55

Pang et al. 2010[37] ANSZ d33 = 295 1.61 45.5 84
Park et al. 2006[38] KNN-BZ d33 = 400 2 57.4 48
Cho et al. 2007[39] KNN-BT d33 = 225 1.06 36.0
Park et al. 2007[40] KNN-ST d33 = 220 1.45 40.0 70
Zhao et al. 2007[41] KNN-CT d33 = 241 1.32 41.0
Zhang et al. 2006[42] LNKN d33 = 314 ~700 41.2
Saito et al. 2004[43] KNN-LS d33 = 270 1.38 50.0
Saito et al. 2004[43] LF4 d33 = 300 1.57
Tanaka et al. 2009[36] Oriented LF4 d33 = 416 1.57 61.0
Pang et al. 2010[37] ANSZ d33 = 295 1.61 45.5 84
Park et al. 2006[38] KNN-BZ d33 = 400 2 57.4 48
Cho et al. 2007[44] KNN-BT d33 = 225 1.06 36.0
Park et al. 2007[40] KNN-ST d33 = 220 1.45 40.0 70
Maurya et al. 2013[45] KNN-CT d33 = 241 1.32 41.0
Maurya et al. 2013[45] NBT-BT (001) Textured samples d33 = 322 ...
Gao et al. 2008[46] NBT-BT-KBT (001) Textured samples d33 = 192
Zou et al. 2016[47] NBT-KBT (001) Textured samples d33 = 134 kp= 35
Saito et al. 2004[43] NBT-KBT (001) Textured samples d33 = 217 kp = 61
Chang et al. 2009[48] KNLNTS (001) Textured samples d33 = 416 kp = 64
Chang et al. 2011[49] KNNS (001) Textured samples d33 = 208 kp = 63
Hussain et al. 2013[50] KNLN (001) Textured samples d33 = 192 kp = 60
Takao et al. 2006[51] KNNT (001) Textured samples d33 = 390 kp = 54
Li et al. 2012[52] KNN 1 CuO (001) Textured samples d33 = 123 kp = 54
Cho et al. 2012[53] KNN-CuO (001) Textured samples d33 = 133 kp = 46
Hao et al. 2012[54] NKLNT (001) Textured samples d33 = 310 kp = 43
Gupta et al. 2014[55] KNLN (001) Textured samples d33 = 254
Hao et al. 2012[54] KNN (001) Textured samples d33 = 180 kp = 44
Bai et al. 2016[56] BCZT (001) Textured samples d33 = 470 kp = 47
Ye et al. 2013[57] BCZT (001) Textured samples d33 = 462 kp = 49
Schultheiß et al. 2017 [58] BCZT-T-H (001) Textured samples d33 = 580
OMORI et al. 1990[59] BCT (001) Textured samples d33 = 170
Chan et al. 2008[60] Pz34 (doped PbTiO3) d15 = 43.3 ε33 = 237 k31 = 4.6 700
d31 = -5.1 ε33 = 208 k33 = 39.6
d33 = 46 k15 = 22.8
kp = 7.4
Lee et al. 2009[61] BNKLBT d33 = 163 εr = 766 k31 = 0.188 142
ε33 = 444.3 kt = 0.524
kp = 0.328
Sasaki et al. 1999[62] KNLNTS εr = 1156 k31 = 0.26 80
ε33 = 746 kt = 0.32
kp = 0.43
Takenaka et al. 1991[63] (Bi0.5Na0.5)TiO3 (BNT)-based BNKT d31 = 46 εr = 650 kp = 0.27
d33 = 150 k31 = 0.165
Tanaka et al. 1960[64] (Bi0.5Na0.5)TiO3 (BNT)-based BNBT d31 = 40 εr = 580 k31 = 0.19
d33 = 12.5 k33 = 0.55
Hutson 1960[65] CdS d15 = -14.35
d31 = -3.67
d33 = 10.65
Schofield et al. 1957[66] CdS d31 = -1.53
d33 = 2.56
Egerton et al. 1959[67] BaCaOTi d31 = -50 k15 = 0.19 400
d33 = 150 k31 = 0.49
k33 = 0.325
Ikeda et al. 1961[68] Nb2O6Pb d31 = -11 kr = 0.07 11
d33 = 80 k31 = 0.045
k33 = 0.042
Ikeda et al. 1962[69] C6H17N3O10S d23 = 84 k21 = 0.18
d21 = 22.7 k22 = 0.18
d25 = 22 k23 = 0.44
Brown et al. 1962[70] BaTiO3 (95%) BaZrO3 (5%) k15 = 0.15 200
d31 = -60 k31 = 0.40
d33 = 150 k33 = 0.28
Huston 1960[65] BaNb2O6 (60%) Nb2O6Pb (40%) d31 = -25 kr = 0.16
Baxter et al. 1960[71] BaNb2O6 (50%) Nb2O6Pb (50%) d31= -36 kr = 0.16
Pullin 1962[72] BaTiO3 (97%) CaTiO3 (3%) d31 = -53 ε33 = 1390 k15 = 0.39
d33 = 135 k31 = 0.17
k33 = 0.43
Berlincourt et al. 1960[73] BaTiO3 (95%) CaTiO3 (5%) d15 = -257 ε33 = 1355 k15 = 0.495 500
d31 = -58 k31 = 0.19
d33 = 150 k33 = 0.49
kr = 0.3
Berlincourt et al. 1960[73] BaTiO3 (96%) PbTiO3 (4%) d31 = -38 ε33 = 990 k15 = 0.34
d33 = 105 k31 = 0.14
k33 = 0.39
Jaffe et al. 1955[74] PbHfO3 (50%) PbTiO3 (50%) d31 = -54 kr = 0.38
Kell 1962[75] Nb2O6Pb (80%) BaNb2O6 (20%) d31 = 25 kr = 0.20 15
Brown et al. 1962[70] Nb2O6Pb (70%) BaNb2O6 (30%) d31 = -40 ε33 = 900 k31 = 0.13 350
d33 = 100 k33 = 0.3
kr = 0.24
Berlincourt et al. 1960[76] PbTiO3 (52%) PbZrO3 (48%) d15 = 166 k15 = 0.40 1170
d31 = -43 k31 = 0.17
d33 = 110 k33 = 0.43
kr = 0.28
Berlincourt et al. 1960[77] PbTiO3 (50%) lead Zirconate (50%) d15 = 166 k15 = 0.504 950
d31 = -43 k31 = 0.23
d33 = 110 k33 = 0.546
kr = 0.397
Egerton et al. 1959[67] KNbO3 (50%) NaNbO3 (50%) d31 = -32 140
d33 = 80 k31 = 0.21
k33 = 0.51
Brown et al. 1962[70] NaNbO3 (80%) Cd2Nb2O7 (20%) d31 = -80 ε33 = 2000 k31 = 0.17
d33 = 200 k33 = 0.42
kr = 0.30
Schofield et al. 1957[66] BaTiO3 (95%) CaTiO3 (5%) CoCO3 (0.25%) d31 = -60 ε33 = 1605 kr = 0.33
Pullin 1962[72] BaTiO3 (80%) PbTiO3 (12%) CaTiO3 (8%) d31 = -31 k31 = 0.15 1200
d33 = 79 k33 = 0.41
kr = 0.24
Defaÿ 2011[78] AlN (Pt-Mo) d31 = -2.5
Shibata et al. 2011[79] KNN(Pt-Pt) <001> d31 = -96.3 εr = 1100
d33 = 138.2
Sessler 1981[80] PVDF d31 = 17.9 k31 = 10.3
d32 = 0.9 k33 = 12.6
d33 = -27.1
Ren et al. 2017[81] PVDF d31 = 23 εr = 106
d32 = 2
d33 = -21
Tsubouchi et al. 1981[82] Epi AlN/Al2O3 <001> d33 = 5.53 ε33 = 9.5 kt = 6.5 2490
Nanomaterials
Reference Material Structure Piezoelectric coefficients, d (pC/N) Characterization method Size (nm)
Ke et al. 2008[83] NaNbO3 nanowire d33 = 0.85-4.26 pm/V PFM d = 100
Wang et al. 2008[84] KNbO3 nanowire d33 = 0.9 pm/V PFM d = 100
Zhang et al. 2004[85] PZT nanowire PFM d = 45
Zhao et al. 2004[86] ZnO nanobelt d33 = 14.3-26.7 pm/V PFM w = 360 t = 65
Luo et al. 2003[87] PZT nanoshell d33 = 90 pm/V PFM d = 700 t = 90
Yun et al. 2002[88] BaTiO3 nanowire d33 = 0.5 pm/V PFM d = 120
Lin et al. 2008[89] CdS nanowire Bending with AFM tip d = 150
Wang et al. 2007[90] PZT nanofiber piezoelectric voltage constant~0.079 Vm/N Bending using a tungsten probe d = 10
Wang et al. 2007[91] BaTiO3 - d33 = 45 pC/N Direct tensile test d ~ 280
Jeong et al. 2014[92] Alkaline niobate (KNLN) film d33 = 310 pC/N -
Park et al. 2010[93] BaTiO3 Thin film d33 = 190 pC/N
Stoppel et al. 2011[94] AlN Thin film d33 =5 pC/N AFM
Lee et al. 2017[95] WSe2 2D nanosheet d11 = 3.26 pm/V
Zhu et al. 2014[96] MoS2 Free standing layer e11 = 2900pc/m AFM
Zhong et al. 2017[97] PET/EVA/PET film d33 = 6300 pC/N

References

  1. ↑ Liu, Huicong; Zhong, Junwen; Lee, Chengkuo; Lee, Seung-Wuk; Lin, Liwei (December 2018). "A comprehensive review on piezoelectric energy harvesting technology: Materials, mechanisms, and applications" (in en). Applied Physics Reviews 5 (4): 041306. doi:10.1063/1.5074184. ISSN 1931-9401. Bibcode: 2018ApPRv...5d1306L. 
  2. ↑ Hutson, Andrew R. "Piezoelectric devices utilizing aluminum nitride." U.S. Patent 3,090,876, issued May 21, 1963.
  3. ↑ Cook, W. R.; Berlincourt, D. A.; Scholz, F. J. (May 1963). "Thermal Expansion and Pyroelectricity in Lead Titanate Zirconate and Barium Titanate". Journal of Applied Physics 34 (5): 1392–1398. doi:10.1063/1.1729587. ISSN 0021-8979. Bibcode: 1963JAP....34.1392C. 
  4. ↑ Warner, A. W.; Onoe, M.; Coquin, G. A. (December 1967). "Determination of Elastic and Piezoelectric Constants for Crystals in Class (3m)". The Journal of the Acoustical Society of America 42 (6): 1223–1231. doi:10.1121/1.1910709. ISSN 0001-4966. Bibcode: 1967ASAJ...42.1223W. 
  5. ↑ Smith, R. T.; Welsh, F. S. (May 1971). "Temperature Dependence of the Elastic, Piezoelectric, and Dielectric Constants of Lithium Tantalate and Lithium Niobate". Journal of Applied Physics 42 (6): 2219–2230. doi:10.1063/1.1660528. ISSN 0021-8979. Bibcode: 1971JAP....42.2219S. 
  6. ↑ Yamada, Tomoaki; Niizeki, Nobukazu; Toyoda, Hiroo (February 1967). "Piezoelectric and Elastic Properties of Lithium Niobate Single Crystals". Japanese Journal of Applied Physics 6 (2): 151–155. doi:10.1143/jjap.6.151. ISSN 0021-4922. Bibcode: 1967JaJAP...6..151Y. 
  7. ↑ Yamada, Tomoaki; Iwasaki, Hiroshi; Niizeki, Nobukazu (September 1969). "Piezoelectric and Elastic Properties of LiTaO3: Temperature Characteristics". Japanese Journal of Applied Physics 8 (9): 1127–1132. doi:10.1143/jjap.8.1127. ISSN 0021-4922. Bibcode: 1969JaJAP...8.1127Y. 
  8. ↑ Cao, Hu; Luo, Haosu (January 2002). "Elastic, Piezoelectric and Dielectric Properties of Pb(Mg 1/3 Nb 2/3 )O 3 -38%PbTiO 3 Single Crystal". Ferroelectrics 274 (1): 309–315. doi:10.1080/00150190213965. ISSN 0015-0193. Bibcode: 2002Fer...274..309C. https://scholarworks.montana.edu/xmlui/handle/1/9713. 
  9. ↑ Badel, A.; Benayad, A.; Lefeuvre, E.; Lebrun, L.; Richard, C.; Guyomar, D. (April 2006). "Single crystals and nonlinear process for outstanding vibration-powered electrical generators". IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 53 (4): 673–684. doi:10.1109/tuffc.2006.1611027. ISSN 0885-3010. PMID 16615571. 
  10. ↑ Kobiakov, I.B. (July 1980). "Elastic, piezoelectric and dielectric properties of ZnO and CdS single crystals in a wide range of temperatures". Solid State Communications 35 (3): 305–310. doi:10.1016/0038-1098(80)90502-5. ISSN 0038-1098. Bibcode: 1980SSCom..35..305K. 
  11. ↑ Zgonik, M.; Bernasconi, P.; Duelli, M.; Schlesser, R.; Günter, P.; Garrett, M. H.; Rytz, D.; Zhu, Y. et al. (September 1994). "Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals". Physical Review B 50 (9): 5941–5949. doi:10.1103/physrevb.50.5941. ISSN 0163-1829. PMID 9976963. Bibcode: 1994PhRvB..50.5941Z. 
  12. ↑ 12.0 12.1 12.2 12.3 12.4 12.5 12.6 12.7 Zgonik, M.; Bernasconi, P.; Duelli, M.; Schlesser, R.; Günter, P.; Garrett, M. H.; Rytz, D.; Zhu, Y. et al. (September 1994). "Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals". Physical Review B 50 (9): 5941–5949. doi:10.1103/physrevb.50.5941. ISSN 0163-1829. PMID 9976963. Bibcode: 1994PhRvB..50.5941Z. 
  13. ↑ "LiNbO3 Properties". https://unitedcrystals.com/LiNbO3Prop.html. 
  14. ↑ Li, Fei; Zhang, Shujun; Xu, Zhuo; Wei, Xiaoyong; Luo, Jun; Shrout, Thomas R. (2010-04-15). "Investigation of Electromechanical Properties and Related Temperature Characteristics in Domain-Engineered Tetragonal Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 Crystals". Journal of the American Ceramic Society 93 (9): 2731–2734. doi:10.1111/j.1551-2916.2010.03760.x. ISSN 0002-7820. 
  15. ↑ 15.0 15.1 15.2 15.3 Zhang, Shujun; Laurent, Lebrun; Rhee, Sorah; Randall, Clive A.; Shrout, Thomas R. (2002-07-29). "Shear-mode piezoelectric properties of Pb(Yb1/2Nb1/2)O3–PbTiO3 single crystals". Applied Physics Letters 81 (5): 892–894. doi:10.1063/1.1497435. ISSN 0003-6951. Bibcode: 2002ApPhL..81..892Z. 
  16. ↑ 16.0 16.1 16.2 Zhang, Shujun; Randall, Clive A.; Shrout, Thomas R. (July 2004). "Dielectric, piezoelectric and elastic properties of tetragonal BiScO3-PbTiO3 single crystal with single domain". Solid State Communications 131 (1): 41–45. doi:10.1016/j.ssc.2004.04.016. ISSN 0038-1098. Bibcode: 2004SSCom.131...41Z. 
  17. ↑ Yamashita, Yohachi; Harada, Kouichi (1997-09-30). "Crystal Growth and Electrical Properties of Lead Scandium Niobate-Lead Titanate Binary Single Crystals". Japanese Journal of Applied Physics 36 (Part 1, No. 9B): 6039–6042. doi:10.1143/jjap.36.6039. ISSN 0021-4922. Bibcode: 1997JaJAP..36.6039Y. 
  18. ↑ Yasuda, N; Ohwa, H; Kume, M; Hayashi, K; Hosono, Y; Yamashita, Y (July 2001). "Crystal growth and electrical properties of lead indium niobate–lead titanate binary single crystal". Journal of Crystal Growth 229 (1–4): 299–304. doi:10.1016/s0022-0248(01)01161-7. ISSN 0022-0248. Bibcode: 2001JCrGr.229..299Y. 
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  94. ↑ Stoppel, F.; Schröder, C.; Senger, F.; Wagner, B.; Benecke, W. (2011). "AlN-based piezoelectric micropower generator for low ambient vibration energy harvesting". Procedia Engineering 25: 721–724. doi:10.1016/j.proeng.2011.12.178. ISSN 1877-7058. 
  95. ↑ Lee, Ju-Hyuck; Park, Jae Young; Cho, Eun Bi; Kim, Tae Yun; Han, Sang A.; Kim, Tae-Ho; Liu, Yanan; Kim, Sung Kyun et al. (2017-06-06). "Reliable Piezoelectricity in Bilayer WSe2 for Piezoelectric Nanogenerators". Advanced Materials 29 (29): 1606667. doi:10.1002/adma.201606667. ISSN 0935-9648. PMID 28585262. Bibcode: 2017AdM....2906667L. 
  96. ↑ Zhu, Hanyu; Wang, Yuan; Xiao, Jun; Liu, Ming; Xiong, Shaomin; Wong, Zi Jing; Ye, Ziliang; Ye, Yu et al. (2014-12-22). "Observation of piezoelectricity in free-standing monolayer MoS2". Nature Nanotechnology 10 (2): 151–155. doi:10.1038/nnano.2014.309. ISSN 1748-3387. PMID 25531085. 
  97. ↑ Zhong, Junwen; Zhong, Qize; Zang, Xining; Wu, Nan; Li, Wenbo; Chu, Yao; Lin, Liwei (July 2017). "Flexible PET/EVA-based piezoelectret generator for energy harvesting in harsh environments". Nano Energy 37: 268–274. doi:10.1016/j.nanoen.2017.05.034. ISSN 2211-2855. 



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