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Piezoelectricity and Ferroelectricity Phenomena and Properties

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Piezoelectricity and Ferroelectricity Phenomena and Properties Piezoelectricity and ferroelectricity Phenomena and properties Prof.Mgr.Ji ří Erhart, Ph.D. Department of Physics FP TUL What is the phenomenon about? • Metallic membrane with „something strange“ • LEDs flash, why? J.Erhart: Demonstrujeme piezoelektrický jev, Matematika, fyzika, informatika 20 (2010) 106-109 FPM - Piezoelectricity 1 2 History 1880, 1881 - Pierre a Jacques Curie, discovery of piezoelectricity, tourmaline and quartz 1917 – A.Langevin – ultrasound generation, sonar 1921 – ferroelectricity - J.Valasek: Piezoelectricity and allied phenomena in Salt, Phys.Rev. 17 (1921) 475 1926 – W.Cady – frequency stabilization of oscillator circuit by the quartz resonator 1944-1946 – USA, SSSR, Japonsko – BaTiO 3 ferroelectric ceramics 1954 – B.Jaffe et al – PZT ceramics 60. léta – LiNbO 3 and LiTaO 3 single crystals 70.léta – ferroelectric polymer PVDF 80.léta – piezoelectric composites 90.léta – domain engineering in PZN-PT, PMN-PT single crystals FPM – Piezoelectricity 1 3 Predecessors of piezoelectricity Pyroelectricity tourmaline = lapis electricus (Na,Ca)(Mg,Fe) 3B3Al 6Si 6(O,OH,F) 31 Franz Ulrich Theodor Aepinus Tourmaline crystal. Carl Linnaeus (1707 – 1778) (1724 – 1802) – polar phenomenon David Brewster – “pyroelectricity” 1824 pyros=ohe ň David Brewster (1781 – 1868) FPM - Piezoelectricity 1 4 Pyroelectricity A.C.Becquerel William Thomson (Lord Kelvin) first pyroelectricity measurement first pyroelectricity theory 1828 1878, 1893 ∆ === ⋅⋅⋅ ∆θ PS p William Thomson, Antoine César Lord Kelvin Becquerel (1824 – 1907) (1788 –1878) FPM - Piezoelectricity 1 5 Piezoelectricity discovery Tourmaline crystal, 1880 8.4.1880 Société minéralogique de France 24.8.1880 Académie des Sciences ∆P = d ⋅⋅⋅T Paul-Jacques Pierre Curie Curie (1859 – 1906) (1856 – 1941) Curie J, Curie P (1880) Développement, par pression, de l’électricité polaire dans les cristaux hémièdres à faces inclinées. Comptes rendus de l’Académie des Sciences 91: 294; 383. Curie J, Curie P (1881) Contractions et dilatations produites par des tensions électriques dans les cristaux hémièdres à faces inclinées. Comptes rendus de l’Académie des Sciences 93: 1137-1140. FPM - Piezoelectricity 1 6 Phenomenon properties • Linear phenomenon, charge is independent from crystal length, it depends on the electrode area • Phenomenon exists due to crystal anisotropy (polar axes), amorphous materials are not piezoelectric Curie’s principle Symmetry elements of external field must be included in the phenomenon symmetry. Crystal under the influence of external field exhibits only symmetry elements common to the symmetry of crystal itself and of the external field. Example: mechanical pressure along [111] direction exerted on the cubic crystal with m3m symmetry causes symmetry reduction of deformed crystal to 3m symmetry class FPM - Piezoelectricity 1 7 Piezoelectricity Direct phenomenon mechanical pressure → electrical charge Converse phenomenon electric field → mechanical deformation It is limited to certain crystallographic symmetry classes (20 from 32 classes) ,1 2, m, 222 , mm2, 4, 4, 422 , 4mm, 42m, 3, 32 , 3m, 6, 6, 622 , 6mm, 62m, 43m, 23 Example: SiO 2 (quartz) symmetry 32 FPM - Piezoelectricity 1 8 Measurement technique Direct phenomenon (Brothers Curie) • Thompson’s electrometer • Null method ∆Q=V∆C (Daniel’s cell – 1.12V, 1836) FPM - Piezoelectricity 1 9 Measurement technique Converse phenomenon (Brothers Curie) • Holtz’s machine (induction electricity, HV) • Strain measured by the direct effect, optically FPM - Piezoelectricity 1 10 Piezoelectricity origin Brothers Curie – molecular theory Charges generated at the compression (a) and tension (b) of quartz crystal basic unit FPM - Piezoelectricity 1 11 First theory and application of piezoelectricity Tensor analysis developed for the crystal anisotropy description 1890 Woldemar Voigt: Lehrbuch der Kristallographie, Teubner Verlag 1910 First application – electrometer, radioactivity study (Maria Skłodowska-Curie) Woldemar Voigt (1850 –1919) Maria Skłodowska- Curie’s electrometer Curie (1867 – 1934) FPM - Piezoelectricity 1 12 Coupled field phenomena Heckmann’s diagram Piezoelectricity = E + Sλ sλµ Tµ diλ Ei Jonas Ferdinand Gabriel Lippmann = + ε T (1845 –1921) Di diµTµ ij E j = D + Sλ sλµ Tµ giλ Di = − + β T Ei giµTµ ij D j FPM - Piezoelectricity 1 13 Ferroelectricity Joseph Valasek, 1920, Rochelle Salt NaKC 4H4O6.4H 2O Joseph Valasek (1897-1993) Hysteresis loop of Rochelle Salt – dry crystal, 0oC Valasek J (1921) Piezoelectricity and allied phenomena in Rochelle salt. Phys. Rev. 17: 475-481 FPM - Piezoelectricity 1 14 Electromechanical phenomena Direct conversion between mechanical and electrical energy • Linear effects – Piezo- and Pyroelectricity • Nonlinear effects - Ferroelectricity, Electrostriction Analogy in magnetic materials • Piezomagnetic properties, magnetostriction, magnetoelectric effect, etc. FPM - Piezoelectricity 1 15 Crystallographic constraints for piezoelectricity Noncentrosymmetric classes (except of 432 ) 20 piezoelectric crystallographic classes • Polar classes (10) – singular polar axis 1, 2, m, mm2, 4, 4mm, 3, 3m, 6, 6mm • Polar-neutral classes (10) – multiple polar axes 222, 4, 422, 42m, 32, 6, 622, 6m2, 43m, 23 FPM - Piezoelectricity 1 16 Equations of state Example: piezoelectricity = E + = D + Sµ sµν Tν d kµ Ek Sµ sµν Tν g kµ Dk = + εT = − + βT Di diνTν ik Ek Ei giνTν ik Dk = E − = D − Tµ cµν Sν ekµ Ek Tµ cµν Sν hkµ Dk = + ε S = − + βS Di eiν Sν ik Ek Ei hiν Sν ik Dk FPM - Piezoelectricity 1 17 Piezoelectric coefficients Different coefficients due to the choice of independent variables FPM - Piezoelectricity 1 18 Material property anisotropy d33 surface PS[001] T PbTiO3 – 4mm Maximum 3 2 2 d33 l3 +(d 31 +d 15 )l 3(l 1 +l 2 ) 83.7pC/N for θ = 0 o, i.e. [001] l1=sin( θ)cos( φ), l 2=sin( θ)sin( φ), l 3=cos( θ) C d33 = 83.7, d 31 = -27.2, d 15 = 60.2 [pC/N] FPM - Piezoelectricity 1 19 Material property anisotropy d33 surface PS[001] T BaTiO3 – 4mm Maximum o 3 2 2 224pC/N for θ = 51 d33 l3 +(d 31 +d 15 )l 3(l 1 +l 2 ) l =sin( θ)cos( φ), l =sin( θ)sin( φ), l =cos( θ) 1 2 3 90pC/N for [001] C d33 = 90, d 31 = -33.4, d 15 = 564 [pC/N] 221pC/N for [111] C FPM - Piezoelectricity 1 20 Pyroelectricity Direct effect Temperature change → electric charge Converse effect (electrocaloric effect) Electric field → heat generation or absorption Anisotropy Example: Lithium tetraborate Li 2B4O7, symmetry 4mm FPM - Piezoelectricity 1 21 Crystallographic constraints for pyroelectricity Polar symmetry classes (10) – singular polar axis 1, 2, m, mm2, 4, 4mm, 3, 3m, 6, 6mm Pyroelectric polarization of material (dipole moment) – polar axis direction FPM - Piezoelectricity 1 22 Electrostriction • Nonlinear effect Deformation proportional to the square of electric field • No constraints on the material symmetry, effect exists in all materials FPM - Piezoelectricity 1 23 Electrostriction Nonlinear equations of state = + Sij dkij Ek Qijkl Pk Pl Without crystallographic limits! All materials exhibit electrostrictive properties FPM - Piezoelectricity 1 24 Electrostriction in cubic materials Electrostrictive coefficients Q11 , Q12 , Q44 S Q Q Q 0 0 0 2 1 11 12 12 P1 2 S2 Q12 Q11 Q12 0 0 0 P2 S Q Q Q 0 0 0 2 3 === 12 12 11 P3 S4 0 0 0 Q44 0 0 P P 2 3 S5 0 0 0 0 Q44 0 P1P3 S6 0 0 0 0 0 Q44 P1P2 FPM - Piezoelectricity 1 25 Ferroelectricity Spontaneous dipole moments = pyroelectricity with switchable polarization Electric analogy of permanent magnets Characteristic properties • Ferroelectric domains and domain walls • Hysteresis loop D-E (S-E) FPM - Piezoelectricity 1 26 Hierarchy of electromechanical phenomena Piezo- SiO 2, GaPO 4, AlPO 4, ... Pyro- Li 2B4O7, ... BaTiO , PbTiO , PZT, Ferro- 3 3 KNbO 3, TGS, KDP, ... FPM - Piezoelectricity 1 27 Ferroelectricity Spontaneous existence of polarization (and spontaneous strain at the same time) - structural phase transition Ferroelectric/ferroelastic domains - orientation domain states Domain walls Hysteresis FPM - Piezoelectricity 1 28 BaTiO3 – paraelectric phase Perovskite structure A2+ B4+ O2- FPM - Piezoelectricity 1 29 BaTiO3 – ferroelectric phase Several orientation states exist for the spontaneous polarization m3m 4mm mm2 3m FPM - Piezoelectricity 1 30 Domains, domain walls Domain – space continuous region with the same orientation of the spontaneous dipole moment (polarization) Domain walls – interfaces between domains • Charged walls • Neutral walls Ferroelectric domains exist in ferroelectric phase Phase transition – Curie temperature TC FPM - Piezoelectricity 1 31 D-E a S-E hysteresis loops T. Liu, C. S. Lynch: Domain engineered relaxor ferroelectric single crystals Continuum Mech. Thermodyn. 18 (2006) 119–135 FPM - Piezoelectricity 1 32 Remanent polarization PS, Pr, EC coercive field FPM - Piezoelectricity 1 33 Mechanism of domain reorientation FPM - Piezoelectricity 1 34 Remanent deformation Ferroelasticity in ferroelectric materials FPM - Piezoelectricity 1 35 → Domains in BaTiO3 ceramics m3m 4mm Domain structure evolution during heating of BaTiO 3 ceramics over the Curie temperature (a) Temperature gradient parallel to the domain walls (b) Temperature gradient perpendicular to the domain walls Sang-Beom Kim, Doh-Yeon Kim: J. Am. Ceram. Soc., 83 [6] 1495–98 (2000) FPM - Piezoelectricity 1 36 → Domains in BaTiO3 ceramics m3m 4mm Etched surface of BaTiO 3 ceramics a) Herringbone and chessboard pattern b) Band structure of DW’s, domains continuously cross the grain boundaries G.Arlt, P.Sasko: J.Appl.Phys. 51 (1980)
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