Ferroelectricity. Phase transition. Material properties BaTiO 3 DKDP KDP PZN-PT(9%) PMN-PT(30%) PMN-PT(40%) 4/1/2016 Physics 403 Spring 2016 1
Ferroelectricity. outline Ferroelectricity. Definition Discovery Main properties Phenomenological theory Some materials Relaxors Applications 4/1/2016 Physics 403 Spring 2016 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 4/1/2016 Physics 403 Spring 2016 3
Ferroelectricity: Discovery Rochelle Salt KNaC 4 H 4 O 6 *4H 2 O 4/1/2016 Physics 403 Spring 2016 4
Ferroelectricity: Discovery Rochelle Salt KNaC 4 H 4 O 6 *4H 2 O Fig3. Piezoelectric response as a function of temperature [2] Fig.1. The first published hysteresis loop [1] 1920 1969 Joseph Valasek (1897-1993) University of Minnesota 1. J. Valasek, Phys. Rev. 17, 475 (1921) 2. J. Valasek, Phys. Rev. 19, 478 (1922) 4/1/2016 Physics 403 Spring 2016 5
Ferroelectricity: Two classes of ferroelectrics Order-Disorder Displacement type disorder O Ba P N Ti O O order BaTiO 3 P NaNO 2 4/1/2016 Physics 403 Spring 2016 6
Ferroelectricity: Polarization reversible (P-E hysteresis) PLZST ceramics 40 Sn:Ti = 0.24:0.11 30 20 P ( C/cm 2 ) 10 0-10 -20-30 -40-40 -30-20 -10 0 10 20 30 40 E DC (kv/cm) 4/1/2016 Physics 403 Spring 2016 7
Ferroelectricity: Domains + - Single domain state Multi domain state P net ~0 90 o domains Courtesy of Igor Lukyanchuk http://www.lukyanc.net/stories/nano-worldofdomains 180 o domain pattern Y Lu et al. Science 1997;276:2004-2006 4/1/2016 Physics 403 Spring 2016 8
Ferroelectricity: Domains PMN-PT40% BaTiO 3 Courtesy of Benjamin Vega-Westhoff and Scott Scharfenberg, P403, Fall2009 KH 2 PO 4 Courtesy of Allison Pohl, P403, Fall2009 PMN-PT30% BaTiO 3 191K KD 2 PO 4 Crystal from Forschungsinstitut für mineralische und metallische Werkstoffe -Edelsteine/Edelmetalle 4/1/2016 Physics 403 Spring 2016 9
Ferroelectricity: Landau-Ginzburg phenomenological theory Free energy F P Order parameter (polarization) 1 6 2 1 4 1 ap bp cp... EP 2 4 6 F 0 P To find the equilibrium solution we need to find the minima of FP by solving the equation: Electric field Ignoring higher terms we can get the linear solution: F ap E P 0 P 1 E a Assuming linear dependence of a on temperature we will have: 1 ( T T c ) and finally we will have Curie-Weiss law C C ( T T ) c 4/1/2016 Physics 403 Spring 2016 10
Ferroelectricity: Landau-Ginzburg phenomenological theory 80 In case of b>) (C>0 also) We will have the solution for second order phase transition with two equilibrium points p 0 and p 0. Both F (a.u.) 70 60 50 40 30 E=0 T>T c T=T c these states are equivalent 20 T<T c 10 0-7 0 7 -p 0 P (a.u.) p 0 4/1/2016 Physics 403 Spring 2016 11
Ferroelectricity: Landau-Ginzburg phenomenological theory PLZST ceramics Ps 40 30 40 Sn:Ti = 0.24:0.11 30 40 30 F (a.u.) 20 10 0-10 -20-12 -10-8 -6-4 -2 0 2 4 6 8 10 12 -Ps P (a.u.) P ( C/cm 2 ) 20 10 0-10 -20-30 -40 Pr F (a.u.) 20 10 0-10 -20-12 -10-8 -6-4 -2 0 2 4 6 8 10 12 P (a.u.) Ps F P Including EP term can illustrate the P-E hysteretic behavior 1 2 1 4 1 6 ap bp cp... 2 4 6-40 -30-20 -10 0 10 20 30 40 E DC (kv/cm) EP F (a.u.) 40 30 20 10 0-10 -20-12 -10-8 -6-4 -2 0 2 4 6 8 10 12 4/1/2016 Physics 403 Spring 2016 12 P (a.u.) Pr
Ferroelectricity: Susceptibility P D E P E E (1 ) E E 0 E 0 0 0 0 0 For ferroelectrics >>1 and '/1000 9 6 C=1.9*10 5 ; T CW =385.2K Curie-Weiss law: C ( T ) T CW 00 3 0 400 450 500 T (K) 4/1/2016 Physics 403 Spring 2016 13
Ferroelectricity: Typical ferroelectric materials KH 2 PO 4 E DC =1.2kV/cm Courtesy Max Candocia, P403 Spring 2011 4/1/2016 Physics 403 Spring 2016 14
Ferroelectricity: Typical ferroelectric materials BaTiO 3 cubic rhombohedral orthorhombic tetragonal 4/1/2016 Physics 403 Spring 2016 15
Ferroelectricity: Typical ferroelectric materials T C (K) Ps ( C/cm 2 ) KDP type KH 2 PO 4 123 4.75 KD 2 PO 4 213 4.83 RbH 2 PO 4 147 5.6 Perovskites BaTiO 3 408 26 KNbO3 708 30 PbTiO 3 765 >50 LiTiO 3 938 50 LiNbO 3 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 4/1/2016 Physics 403 Spring 2016 16
Antiferroelectrics <P> ~0 PNZST (film) PLZST (ceramic) Courtesy of E. Colla and City University of Hong Kong 4/1/2016 Physics 403 Spring 2016 17
Antiferroelectricity in BaTiO 3 Courtesy of Alan Selewa and Nathaniel Scheidler (Physics403 class, 2014, unpublished) 4/1/2016 Physics 403 Spring 2016 18
Ferroelectricity: Relaxors - PMN Pb(Mg 1/3 Nb 2/3 )O 3 35 0.35 '/10 3 28 21 14 0.30 0.25 0.20 0.15 1000/ ' 7 0 0.00 150 200 250 300 350 400 450 T (K) Temperature dependencies of the real part of the dielectric constant measured in a broad frequency range: 3*10-3 -10 6 Hz [1,2] 0.10 0.05 1. E.V. Colla et all., J. Phys.: Cond. Matter, 4,3671, (1992) 2. E.V. Colla et all. J. Appl. Phys., 83, 3298, (1998) '/10 3 10 1 10 2 10 3 10 4 10 5 10 6 f (Hz) Frequency dispersion of e at different temperatures 4/1/2016 Physics 403 Spring 2016 19 22 20 18 16 14 12 10 8 6 4 230K 220K 250K 240K
Ferroelectricity: Solid solution relaxor-regular ferroelectric. (PMN) (PMN) (1-x) (PT) (x) phase diagram PT: PbTiO 3, ferroelectric with Curie temperature 763K T c (K) 500 Literature data single crystals ceramics 400 Regular ferroelectric (tetragonal) (PMN) 0.6 (PT) 0.4 Paraelectric (cubic) 300 0.0 0.1 0.2 0.3 0.4 0.5 x (PMN) 0.9 (PT) 0.1 Relaxor state (PMN) 0.7 (PT) 0.3 (pseudocubic) 4/1/2016 Physics 403 Spring 2016 20
Relaxors: Field induced Transition. PMN Pb(Mg 1/3 Nb 2/3 )O 3 Courtesy of Joseph Strehlow and John Whitman 4/1/2016 Physics 403 Spring 2016 21
Relaxors: Field induced Transition. PMN Pb(Mg 1/3 Nb 2/3 )O 3 4/1/2016 Physics 403 Spring 2016 22
Ferroelectricity: Relaxors - some aplications Actuators Transducers Adaptive optics Capacitors Line motors for SFM Transducer stack for ultrasonic sonar application (TRS Ceramics) Material Dielectric constant Piezoelectric coefficient, (pc/n) Electromechanical coupling factor Quartz 4.5 2.3 0.1 Rochelle salt (30C) 9.2 27 0.3 Barium titanate 1700 190 0.52 ceramic Lead zirconate 450 140 060 titanate PZT 45/55 PMN-PT (sc) 4200 2200 0.92-0.94 PZN-PT (sc) 2500 2400 0.91-0.93 Piezoelectric properties of different materials 4/1/2016 Physics 403 Spring 2016 23
Ferroelectricity: Relaxors - some aplications Adaptive optics 4/1/2016 Physics 403 Spring 2016 24
Ferroelectricity: Relaxors - some aplications Ferroelectric RAM Courtesy of 4/1/2016 Physics 403 Spring 2016 25
Ferroelectricity: Relaxors - some aplications Actuators 4/1/2016 Physics 403 Spring 2016 26