Magnetoelectric Interactions in Lead-Based and Lead-Free Composites
Abstract
:1. Introduction
pDk = pdki pTi + pεkn pEn
mBk = mqki mTi + mμkn mHn
Dk = dkiTi + εknEn + αkn Hn
Bk = qkiTi + αknEn + μknHn
2. Progress on Lead–Free Piezoelectric Materials
2.1. NBT-BT Lead-Free Piezoelectric
2.2. NKN Based Lead-Free Piezoelectric
Materials | d33 | kp | k33 | Tc | To–t/Td | Reference |
---|---|---|---|---|---|---|
BaTiO3 | 190 | 0.36 | 0.5 | 115 | 0 | [116] |
BT-BCN | 330 | 0.43 | 80 | -- | [117] | |
NBT-KBT-LBT | 216 | 0.401 | 350 | 160 | [118] | |
NBT-KBT-BT | 183 | 0.367 | 0.619 | 290 | 100 | [119] |
NBT-xBT; x = 6–8% | 122–176 | 0.21–0.36 | 225–228 | 90–105 | [87,120,121,122,123,124] | |
NBT-6BT+7.5L | 208 | 0.368 | 260 | 85 | [125,126] | |
NBT-6BT-2NKN | 30 | 260 | [100,101] | |||
NBT-20KBT (MPB) | 140–190 | 0.27–0.35 | 280–300 | 130–170 | [127,128,129,130,131,132] | |
(K0.5Na0.5)NbO3 (H.P.) | 127 | 0.46 | 0.6 | 420 | [107,108] | |
(K0.5Na0.5)NbO3 | 80 | 0.35 | 0.51 | 420 | 195 | [133] |
NKN-Li (7%) | 240 | 0.45 | 0.64 | 460 | ~20 | [134] |
NKN-LF4(Textured) | 410 | 0.61 | - | 253 | 25 | [91,135] |
NKN-SrTiO3 (5%) | 200 | 0.37 | - | 277 | 27 | [67,68] |
NKN-LiTaO3 (5%) | 200 | 0.36 | - | 430 | 55 | [63] |
NKN-LiNbO3 (6%) | 235 | 0.42 | - | 460 | 70 | [62] |
NKN-LiSbO3 (5%) | 283 | 0.50 | - | 392 | 45 | [64] |
3. Modeling of Piezoelectric Materials
3.1. Single Domain Approximation in Computing the Piezoelectric Coefficients of Ferroelectrics
3.1.1. Lead Titanate
3.1.2. Barium Titanate
3.1.3. LiTaO3
3.1.4. KNbO3
Coefficients | PbTiO3 | BaTiO3 | LiTaO3 | KNbO3 | (Na,K)NbO3 | Na0.5Bi0.5TiO3-BaTiO3 |
---|---|---|---|---|---|---|
a1 | 3.8 × 105 (Т − 479) | 4.124 × 105 (T − 115) | 1.256 × 109 | 4.273 × 105 (T − 377) | ||
a11 (a2) | −7.3 × 107 | 5.328 × 108 | 5.043 × 109 | 6.36 × 108 | ||
a12 | 9.66 × 108 | |||||
a111 | 2.6 × 108 | 1.294 × 109 | 2.81 × 109 | |||
a112 | −1.99 × 109 | |||||
a123 | 6.03 × 109 | |||||
a1111 | 3.863 × 1010 | 1.74 × 1010 | ||||
a1112 | 5.99 × 109 | |||||
a1122 | 2.50 × 1010 | |||||
a1123 | −1.17 × 1010 |
B | PbTiO3 | BaTiO3 | LiTaO3 | KNbO3 | (Na,K)NbO3 | Na0.5Bi0.5TiO3-BaTiO3 | ||||||
Theory | Obser-vation | Theory | Obser-vation | Theory | Obser-vation | Theory | Obser-vation | Theory | Obser-vation | Theory | Obser-vation | |
Ps (С/m2) | 1.5 | 0.26 | 0.26 | 0.5 | 0.45 | 0.42 | ||||||
ε33/ε0 | 75 | 189 | 188 | 46 | 55 | |||||||
ε22/ε0 | 160 | |||||||||||
ε11/ε0 | 1000 | |||||||||||
d31 (10−12m/V) | −11 | −37 | −29.4 | 1.0 | 3.4 | 9.8 | ||||||
d32 (10−12m/V) | −24.3 | −22.3 | ||||||||||
d33 (10−12m/V) | 22 | 25 | 95 | 86.3 | −2.5 | 27.4 | 29.3 |
3.2. Theory of Ferroelectric Solid Solutions (Generalized Lattice Model) [149,150,151,152]
3.2.1. Effective Fields
3.2.2. Generating Functional and Polarization of Solution
3.2.3. Mean Value of a Single Particle Dipole Moment in Effective Field
3.2.4. Polarization of Solid Solution
3.2.5. Parameters of the Components
3.2.6. Susceptibility of Solid Solution
3.2.7. Critical Points of Solid Solutions and Model Parameters
3.2.8. System Ba1−xPbxTiO3
x | 0 | 0.5 | 1.0 |
T(x) | 393 K | 623 K | 763 K |
4. Modeling of Magnetoelectric Composites
pDk = pdki pTi + pεkn pEn
Material | s11 (10−12 m2/N) | s12 (10−12 m2/N) | q11 (10−12 m/A) | q12 (10−12 m/A) | d31 (10−12 m/V) | d33 (10−12 m/V) | ε33/ε0 |
---|---|---|---|---|---|---|---|
PZT | 17.3 | −7.22 | - | - | −175 | 400 | 1750 |
NBT-BT | 7.3 | −3.2 | - | - | −140 | 280 | 2000 |
Mn:NBT-BT | 7.3 | −3.2 | −242 | 483 | 4000 | ||
NKN-BT | 5.55 | −1.04 | −110 | 225 | 1058 | ||
NZFO | 6.5 | −2.4 | −1050 | 210 | - | ||
CFO | 6.5 | −2.4 | −1880 | 556 | |||
Ni | 4.9 | −1.5 | −4140 | 570 |
5. Data on Magnetoelectric Response in 3-0, 2-2, and 1-3 Composites
5.1. ME Effect in Sintered Composites
5.2. ME Effect in 2-2 Composites
Material | |
MnFe2O4 | −5 |
Fe3O4 | 40 |
CoFe2O4 | −110 |
MgFe2O4 | −6 |
Li0.5Fe2.5O4 | −8 |
NiFe2O4 | −26 |
CuFe2O4 | −9 |
YFe5O12 | −2 |
SmFe5O12 | 3.3 |
DyFe5O12 | 1.46 |
EuFe5O12 | 9.48 |
5.3. ME Effect in 1-3 Composites
pur = mur and pTr = mTr at r = pR
6. Conclusions
Acknowledgments
References
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Bichurin, M.; Petrov, V.; Zakharov, A.; Kovalenko, D.; Yang, S.C.; Maurya, D.; Bedekar, V.; Priya, S. Magnetoelectric Interactions in Lead-Based and Lead-Free Composites. Materials 2011, 4, 651-702. https://doi.org/10.3390/ma4040651
Bichurin M, Petrov V, Zakharov A, Kovalenko D, Yang SC, Maurya D, Bedekar V, Priya S. Magnetoelectric Interactions in Lead-Based and Lead-Free Composites. Materials. 2011; 4(4):651-702. https://doi.org/10.3390/ma4040651
Chicago/Turabian StyleBichurin, Mirza, Vladimir Petrov, Anatoly Zakharov, Denis Kovalenko, Su Chul Yang, Deepam Maurya, Vishwas Bedekar, and Shashank Priya. 2011. "Magnetoelectric Interactions in Lead-Based and Lead-Free Composites" Materials 4, no. 4: 651-702. https://doi.org/10.3390/ma4040651