List of piezoelectric materials explained

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], (Bi_1/2Na_1/2) TiO₃ [BNT], (Bi_1/2K_1/2) 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 d_ij 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 (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, 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	BaTiO3 single crystals	[111] (single domain)	d33 = 224
Zgonik et al. 1994	BaTiO3 single crystals	[111] neutral (domain size of 100 ľm)	d33 = 235	ε33 = 1984	k33 = 54.4
Zgonik et al. 1994	BaTiO3 single crystals	[111] neutral (domain size of 60 ľm)	d33 = 241	ε33 = 1959	k33 = 55.9
Zgonik et al. 1994	BaTiO3 single crystals	[111] (domain size of 22 ľm)	d33 = 256	ε33 = 2008	k33 = 64.7
Zgonik et al. 1994	BaTiO3 single crystals	[111] neutral (domain size of 15 ľm)	d33 = 274	ε33 = 2853	k33 = 66.1
Zgonik et al. 1994	BaTiO3 single crystals	[111] neutral (domain size of 14 ľm)	d33 = 289	ε33 = 1962	k33 = 66.7
Zgonik et al. 1994	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	PMNT31-B		1500	ε33 = 4800
Zhang et al. 2002	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	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	PYNT40		d33 = 1200	ε33 = 2700	k31 = 76
			d31 = -500
Zhang et al. 2012	PYNT45		d33 = 2000	ε33 = 2000	k31 = 78
Zhang et al. 2003^[21]	BSPT57		d33 = 1200	ε33 = 3000	k31 = 77
			d31 = -560
Zhang et al. 2003^[22]	BSPT58		d33 = 1400	ε33 = 3200	k31 = 80
			d31 = -670
Zhang et al. 2004	BSPT66		d33 = 440	ε33 = 820	k31 = 52
			d31 = -162
Ye et al. 2008^[23]	BSPT57		d33 = 1150 d31 = -520	ε33 = 3000	k31 = 0.52 k33 = 0.91
Ye et al. 2008	BSPT66		d33 = 440	ε33 = 820	k31 = 0.52 k33 = 0.88
			d31 = -162
Ye et al. 2008	PZNT4.5		d33 = 2000d31 = -970	ε33 = 5200	k31 = 0.50k33 = 0.91
Ye et al. 2008	PZNT8		d31 = -1455	ε33 = 7700	k31 = 0.60 k33 = 0.94
Ye et al. 2008	PZNT12		d33 = 576d31 = -217	ε33 = 870	k31 = 0.52k33 = 0.86
Ye et al. 2008	PMNT33		d33 = 2820 d31 = -1330	ε33 = 8200	k31 = 0.59 k33 = 0.94
Matsubara et al. 2004^[24]	KCN-modified KNN		d33 = 100 d31 = -180	ε33 = 220-330	kp = 33-39	1200
Ryu et al. 2007^[25]	KZT modifiedKNN		d33 = 126	ε33 = 590	kp = 42	58
Matsubara et al. 2005^[26]	KCT modified KNN		d33 = 190	ε33 =	kp = 42	1300
Wang et al. 2007^[27]	Bi2O3 doped KNN		d33 = 127	ε33 = 1309	kp = 28.3
Jiang et al. 2009^[28]	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^[29]	BaTiO3		d15 = 270	ε11 = 1440	k15 = 0.57
			d31 = -79	ε33 = 1680	k31 = 0.49
			d33 = 191		k33 = 0.47
Tang et al. 2011^[30]	BFO		d33 = 37		kt = 0.6
Zhang et al. 1999^[31]	PMN-PT		d31 = -74	ε33 = 1170	k31 = -0.312	283
	PZT-5A		d31 = -171	ε33 = 1700	k31 = 0.34
			d33 = 374		k33 = 0.7
^[32]	PZT-5H		d15 = 741	ε11 = 3130	k15 = 0.68	65
			d31 = -274	ε33 = 3400	k31 = 0.39
			d33 = 593		k33 = 0.75
^[33]	PZT-5K		d33 = 870	ε33 = 6200	k33 = 0.75
Tanaka et al. 2009^[34]	PZN7%PT		d33 = 2400	εr = 6500	k33 = 0.94 kt = 0.55
Pang et al. 2010^[35]	ANSZ		d33 = 295	1.61	45.5	84
Park et al. 2006^[36]	KNN-BZ		d33 = 400	2	57.4	48
Cho et al. 2007^[37]	KNN-BT		d33 = 225	1.06	36.0
Park et al. 2007^[38]	KNN-ST		d33 = 220	1.45	40.0	70
Zhao et al. 2007^[39]	KNN-CT		d33 = 241	1.32	41.0
Zhang et al. 2006^[40]	LNKN		d33 = 314	~700	41.2
Saito et al. 2004^[41]	KNN-LS		d33 = 270	1.38	50.0
Saito et al. 2004	LF4		d33 = 300	1.57
Tanaka et al. 2009	Oriented LF4		d33 = 416	1.57	61.0
Pang et al. 2010	ANSZ		d33 = 295	1.61	45.5	84
Park et al. 2006	KNN-BZ		d33 = 400	2	57.4	48
Cho et al. 2007^[42]	KNN-BT		d33 = 225	1.06	36.0
Park et al. 2007	KNN-ST		d33 = 220	1.45	40.0	70
Maurya et al. 2013^[43]	KNN-CT		d33 = 241	1.32	41.0
Maurya et al. 2013	NBT-BT	(001) Textured samples	d33 = 322		...
Gao et al. 2008^[44]	NBT-BT-KBT	(001) Textured samples	d33 = 192
Zou et al. 2016^[45]	NBT-KBT	(001) Textured samples	d33 = 134		kp= 35
Saito et al. 2004	NBT-KBT	(001) Textured samples	d33 = 217		kp = 61
Chang et al. 2009^[46]	KNLNTS	(001) Textured samples	d33 = 416		kp = 64
Chang et al. 2011^[47]	KNNS	(001) Textured samples	d33 = 208		kp = 63
Hussain et al. 2013^[48]	KNLN	(001) Textured samples	d33 = 192		kp = 60
Takao et al. 2006^[49]	KNNT	(001) Textured samples	d33 = 390		kp = 54
Li et al. 2012^[50]	KNN 1 CuO	(001) Textured samples	d33 = 123		kp = 54
Cho et al. 2012^[51]	KNN-CuO	(001) Textured samples	d33 = 133		kp = 46
Hao et al. 2012^[52]	NKLNT	(001) Textured samples	d33 = 310		kp = 43
Gupta et al. 2014^[53]	KNLN	(001) Textured samples	d33 = 254
Hao et al. 2012	KNN	(001) Textured samples	d33 = 180		kp = 44
Bai et al. 2016^[54]	BCZT	(001) Textured samples	d33 = 470		kp = 47
Ye et al. 2013^[55]	BCZT	(001) Textured samples	d33 = 462		kp = 49
Schultheiß et al. 2017 ^[56]	BCZT-T-H	(001) Textured samples	d33 = 580
OMORI et al. 1990^[57]	BCT	(001) Textured samples	d33 = 170
Chan et al. 2008^[58]	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^[59]	BNKLBT		d33 = 163	εr = 766	k31 = 0.188	142
				ε33 = 444.3	kt = 0.524
					kp = 0.328
Sasaki et al. 1999^[60]	KNLNTS			εr = 1156	k31 = 0.26	80
				ε33 = 746	kt = 0.32
					kp = 0.43
Takenaka et al. 1991^[61]	(Bi0.5Na0.5)TiO3 (BNT)-based BNKT		d31 = 46	εr = 650	kp = 0.27
			d33 = 150		k31 = 0.165
Tanaka et al. 1960^[62]	(Bi0.5Na0.5)TiO3 (BNT)-based BNBT		d31 = 40	εr = 580	k31 = 0.19
			d33 = 12.5		k33 = 0.55
Hutson 1960^[63]	CdS		d15 = -14.35
			d31 = -3.67
			d33 = 10.65
Schofield et al. 1957^[64]	CdS		d31 = -1.53
			d33 = 2.56
Egerton et al. 1959^[65]	BaCaOTi		d31 = -50		k15 = 0.19	400
			d33 = 150		k31 = 0.49
					k33 = 0.325
Ikeda et al. 1961^[66]	Nb2O6Pb		d31 = -11		kr = 0.07	11
			d33 = 80		k31 = 0.045
					k33 = 0.042
Ikeda et al. 1962^[67]	C6H17N3O10S		d23 = 84		k21 = 0.18
			d21 = 22.7		k22 = 0.18
			d25 = 22		k23 = 0.44
Brown et al. 1962^[68]	BaTiO3 (95%) BaZrO3 (5%)				k15 = 0.15	200
			d31 = -60		k31 = 0.40
			d33 = 150		k33 = 0.28
Huston 1960	BaNb2O6 (60%) Nb2O6Pb (40%)		d31 = -25		kr = 0.16
Baxter et al. 1960^[69]	BaNb2O6 (50%) Nb2O6Pb (50%)		d31= -36		kr = 0.16
Pullin 1962^[70]	BaTiO3 (97%) CaTiO3 (3%)		d31 = -53	ε33 = 1390	k15 = 0.39
			d33 = 135		k31 = 0.17
					k33 = 0.43
Berlincourt et al. 1960^[71]	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	BaTiO3 (96%) PbTiO3 (4%)		d31 = -38	ε33 = 990	k15 = 0.34
			d33 = 105		k31 = 0.14
					k33 = 0.39
Jaffe et al. 1955^[72]	PbHfO3 (50%) PbTiO3 (50%)		d31 = -54		kr = 0.38
Kell 1962^[73]	Nb2O6Pb (80%) BaNb2O6 (20%)		d31 = 25		kr = 0.20	15
Brown et al. 1962	Nb2O6Pb (70%) BaNb2O6 (30%)		d31 = -40	ε33 = 900	k31 = 0.13	350
			d33 = 100		k33 = 0.3
					kr = 0.24
Berlincourt et al. 1960^[74]	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^[75]	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	KNbO3 (50%) NaNbO3 (50%)		d31 = -32			140
			d33 = 80		k31 = 0.21
					k33 = 0.51
Brown et al. 1962	NaNbO3 (80%) Cd2Nb2O7 (20%)		d31 = -80	ε33 = 2000	k31 = 0.17
			d33 = 200		k33 = 0.42
					kr = 0.30
Schofield et al. 1957	BaTiO3 (95%) CaTiO3 (5%) CoCO3 (0.25%)		d31 = -60	ε33 = 1605	kr = 0.33
Pullin 1962	BaTiO3 (80%) PbTiO3 (12%) CaTiO3 (8%)		d31 = -31		k31 = 0.15	1200
			d33 = 79		k33 = 0.41
					kr = 0.24
Defaÿ 2011^[76]	AlN (Pt-Mo)		d31 = -2.5
Shibata et al. 2011^[77]	KNN(Pt-Pt)	<001>	d31 = -96.3	εr = 1100
			d33 = 138.2
Sessler 1981^[78]	PVDF		d31 = 17.9		k31 = 10.3
			d32 = 0.9		k33 = 12.6
			d33 = -27.1
Ren et al. 2017^[79]	PVDF		d31 = 23	εr = 106
			d32 = 2
			d33 = -21
Tsubouchi et al. 1981^[80]	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^[81]	NaNbO3	nanowire	d33 = 0.85-4.26 pm/V	PFM	d = 100
Wang et al. 2008^[82]	KNbO3	nanowire	d33 = 0.9 pm/V	PFM	d = 100
Zhang et al. 2004^[83]	PZT	nanowire		PFM	d = 45
Zhao et al. 2004^[84]	ZnO	nanobelt	d33 = 14.3-26.7 pm/V	PFM	w = 360 t = 65
Luo et al. 2003^[85]	PZT	nanoshell	d33 = 90 pm/V	PFM	d = 700 t = 90
Yun et al. 2002^[86]	BaTiO3	nanowire	d33 = 0.5 pm/V	PFM	d = 120
Lin et al. 2008^[87]	CdS	nanowire		Bending with AFM tip	d = 150
Wang et al. 2007^[88]	PZT	nanofiber	piezoelectric voltage constant~0.079 Vm/N	Bending using a tungsten probe	d = 10
Wang et al. 2007^[89]	BaTiO3	-	d33 = 45 pC/N	Direct tensile test	d ~ 280
Jeong et al. 2014^[90]	Alkaline niobate (KNLN)	film	d33 = 310 pC/N	-
Park et al. 2010^[91]	BaTiO3	Thin film	d33 = 190 pC/N
Stoppel et al. 2011^[92]	AlN	Thin film	d33 =5 pC/N	AFM
Lee et al. 2017^[93]	WSe2	2D nanosheet	d11 = 3.26 pm/V
Zhu et al. 2014^[94]	MoS2	Free standing layer	e11 = 2900pc/m	AFM
Zhong et al. 2017^[95]	PET/EVA/PET	film	d33 = 6300 pC/N

Notes and References

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