Ferroelectricity. Phase transition. Material properties
BaTiO3 DKDP
KDP
PZN-PT(9%) PMN-PT(30%) PMN-PT(40%)
4/22/2014 Physics 403 Spring 2014 1 Ferroelectricity. outline
•Ferroelectricity. Definition •Discovery •Main properties •Phenomenological theory • Some materials •Relaxors •Applications
4/22/2014 Physics 403 Spring 2013 2 Ferroelectricity. Definitions.
Ferroelectric Materials. A ferroelectric material is a material that exhibits, over some range of temperature, a spontaneous electric polarization that can be reversed or reoriented by application of an electric field.
An American National Standard IEEE Standard Definitions of Primary Ferroelectric Terms
4/22/2014 Physics 403 Spring 2013 3 Ferroelectricity: Discovery
Rochelle Salt KNaC4H4O6*4H2O
4/22/2014 Physics 403 Spring 2013 4 Ferroelectricity: Discovery
Rochelle Salt KNaC4H4O6*4H2O
Fig3. Piezoelectric Fig.1. The first published hysteresis loop [1] response as a function 1920 1969 of temperature [2] Joseph Valasek (1897-1993) University of Minnesota
1. J. Valasek, Phys. Rev. 17, 475 (1921) 2. J. Valasek, Phys. Rev. 19, 478 (1922)
4/22/2014 Physics 403 Spring 2013 5 Ferroelectricity: Two classes of ferroelectrics Order-Disorder
Displacement type disorder O
Ba P N O Ti O order
BaTiO3 P
NaNO2
4/22/2014 Physics 403 Spring 2013 6 Ferroelectricity: Polarization reversible (P-E hysteresis)
PLZST ceramics
40 Sn:Ti = 0.24:0.11
30
20
)
2 10
0
C/cm
( -10
P -20
-30
-40
-40 -30 -20 -10 0 10 20 30 40 E (kV/cm) DC
4/22/2014 Physics 403 Spring 2013 7 Ferroelectricity: Domains
- Single domain state +
Multi domain state 90o domains Pnet~0
Courtesy of Igor Lukyanchuk http://www.lukyanc.net/stories/nano-worldofdomains
180o domain pattern
Y Lu et al. Science 1997;276:2004-2006 4/22/2014 Physics 403 Spring 2013 8 Ferroelectricity: Domains
PMN-PT40%
BaTiO3 KH2PO4
Courtesy of Benjamin Vega-Westhoff Courtesy of Allison Pohl, P403, and Scott Scharfenberg, P403, Fall2009 Fall2009
PMN-PT30%
BaTiO3 191K KD2PO4
Crystal from Forschungsinstitut für mineralische und metallische Werkstoffe -Edelsteine/Edelmetalle
4/22/2014 Physics 403 Spring 2013 9 Ferroelectricity: Landau-Ginzburg phenomenological theory
Free energy Order parameter (polarization) Electric field 1 1 1 F aP 2 bP 4 cP 6 ... EP P 2 4 6 F To find the equilibrium solution we need to 0 find the minima of FP by solving the equation: P
Ignoring higher terms we can get the linear solution:
F P 1 aP E 0 P E a Assuming linear dependence of a on temperature we will have:
1 C and finally we will have Curie-Weiss law ()TTc C ()TT c
4/22/2014 Physics 403 Spring 2013 10 Ferroelectricity: Landau-Ginzburg phenomenological theory
80
70 In case of b>) (C>0 also) We will 60 have the solution for second order T>Tc 50 E=0 phase transition with two 40
T=Tc F (a.u.) equilibrium points –p0 and p0. Both 30
20 these states are equivalent T 0 -7 0 7 P (a.u.) -p0 p0 4/22/2014 Physics 403 Spring 2013 11 Ferroelectricity: Landau-Ginzburg phenomenological theory Ps PLZST ceramics 40 40 40 Sn:Ti = 0.24:0.11 30 30 30 20 20 20 10 10 F (a.u.) ) F (a.u.) 2 10 0 0 Pr 0 -10 C/cm -10 ( -10 -20 -20 P -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 P (a.u.) -20 P (a.u.) -30 Ps -Ps -40 -40 -30 -20 -10 0 10 20 30 40 E (kV/cm) DC 40 Including EP term can illustrate 30 the P-E hysteretic behavior 20 1 2 1 4 1 6 10 F (a.u.) FP aP bP cP ... EP 2 4 6 0 -10 -20 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 P (a.u.) 4/22/2014 Physics 403 Spring 2013 Pr 12 Ferroelectricity: Susceptibility PE 0 DEPEEEE00000 (1) For ferroelectrics >>1 and ≈ 9 Curie-Weiss law: C=1.9*105; TCW=385.2K C 00 6 (T TCW ) '/1000 3 0 400 450 500 T (K) 4/22/2014 Physics 403 Spring 2013 13 Ferroelectricity: Typical ferroelectric materials KH2PO4 EDC=1.2kV/cm Courtesy Max Candocia, P403 Spring 2011 4/22/2014 Physics 403 Spring 2013 14 Ferroelectricity: Typical ferroelectric materials BaTiO3 cubic rhombohedral orthorhombic tetragonal 4/22/2014 Physics 403 Spring 2013 15 Ferroelectricity: Typical ferroelectric materials 2 TC(K) Ps (C/cm ) KDP type KH2PO4 123 4.75 KD2PO4 213 4.83 RbH2PO4 147 5.6 Perovskites BaTiO3 408 26 KNbO3 708 30 PbTiO3 765 >50 LiTiO3 938 50 LiNbO3 1480 71 Number of publications concerning ferroelectricity. From Jan Fousek “Joseph Valasek and the Discovery of Ferroelectricity” Number of ferroelectric substances discovered in each year. Springer Handbook of Condensed Matter and Materials Data 4/22/2014 Physics 403 Spring 2013 16 Antiferroelectrics ~0 PNZST (film) PLZST (ceramic) Courtesy of E. Colla and 4/22/2014 Physics 403 Spring 2013 17 City University of Hong Kong Antiferroelectricity in BaTiO3 Courtesy of Alan Selewa and Nathaniel Scheidler (2014, unpublished) 4/22/2014 Physics 403 Spring 2013 18 Ferroelectricity: Relaxors - PMN Pb(Mg1/3 Nb2/3)O3 35 0.35 28 0.30 0.25 3 ' 21 0.20 '/10 14 0.15 1000/ 0.10 7 22 0.05 20 18 0 0.00 250K 150 200 250 300 350 400 450 16 T (K) 3 14 Temperature dependencies of the 12 240K '/10 real part of the dielectric constant 10 measured in a broad frequency 230K range: 3*10-3 -106 Hz [1,2] 8 220K 6 4 1. E.V. Colla et all., J. Phys.: Cond. Matter, 4,3671, (1992) 1 2 3 4 5 6 2. E.V. Colla et all. J. Appl. Phys., 83, 3298, (1998) 10 10 10 10 10 10 f (Hz) Frequency dispersion of e’ at different temperatures 4/22/2014 Physics 403 Spring 2013 19 Ferroelectricity: Solid solution relaxor-regular ferroelectric. PT: PbTiO3, ferroelectric with (PMN)0.7(PT)0.3 (PMN)(1-x)(PT)(x) phase diagram Curie temperature 763K 500 Literature data single crystals Regular ferroelectric ceramics (tetragonal) 400 (PMN)0.6(PT)0.4 (K) c T Paraelectric 300 (cubic) 0.0 0.1 0.2 0.3 0.4 0.5 x (PMN) (PT) 0.9 0.1 (PMN) (PT) “Relaxor”state 0.7 0.3 (pseudocubic) 4/22/2014 Physics 403 Spring 2013 20 Ferroelectricity: Relaxors - some aplications Actuators Transducers Adaptive optics Capacitors Transducer stack for Line motors for SFM ultrasonic sonar application (TRS Ceramics) Material Dielectric Piezoelectric Electromechanical constant coefficient, (pC/n) coupling factor Quartz 4.5 2.3 0.1 Rochelle salt (30C) 9.2 27 0.3 Piezoelectric Barium titanate 1700 190 0.52 ceramic properties of different Lead zirconate 450 140 060 materials titanate PZT 45/55 PMN-PT (sc) 4200 2200 0.92-0.94 PZN-PT (sc) 2500 2400 0.91-0.93 4/22/2014 Physics 403 Spring 2013 21