Ferroelectricity. Phase transition. Material properties. 4/12/2011 Physics 403 Spring

Transcription

1 Ferroelectricity. Phase transition. Material properties 4/12/211 Physics 43 Spring 211 1

2 Ferroelectricity. outline Ferroelectricity. Definition Discovery Main properties Phenomenological theory Some materials Relaxors Applications 4/12/211 Physics 43 Spring 211 2

3 Ferroelectricity. Definitions. 2.1 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 4/12/211 Physics 43 Spring 211 3

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] Joseph Valasek ( ) University of Minnesota 1. J. Valasek, Phys. Rev. 17, 475 (1921) 2. J. Valasek, Phys. Rev. 19, 478 (1922) 4/12/211 Physics 43 Spring 211 4

5 Ferroelectricity: Discovery Rochelle Salt KNaC 4 H 4 O 6 *4H 2 O 4/12/211 Physics 43 Spring 211 5

6 Ferroelectricity: Two classes of ferroelectrics Displacement type Order-Disorder disorder O Ba P N Ti O O order BaTiO 3 P NaNO 2 4/12/211 Physics 43 Spring 211 6

7 Ferroelectricity: Polarization reversible (P-E E hysteresis) PLZST ceramics 4 Sn:Ti =.24: P (μc/cm 2 ) E DC (kv/cm) 4/12/211 Physics 43 Spring 211 7

8 Ferroelectricity: Domains - Single domain state + Multi domain state P net ~ 9 o domains Courtesy of Igor Lukyanchuk 18 o domain pattern Y Lu et al. Science 1997;276: /12/211 Physics 43 Spring 211 8

9 Ferroelectricity: Domains PMN-PT4% BaTiO 3 Courtesy of Benjamin Vega-Westhoff and Scott Scharfenberg, P43, Fall29 KH 2 PO 4 Courtesy of Allison Pohl, P43, Fall29 PMN-PT3% BaTiO 3 191K KD 2 PO 4 Crystal from Forschungsinstitut für mineralische und metallische Werkstoffe -Edelsteine/Edelmetalle 4/12/211 Physics 43 Spring 211 9

10 Ferroelectricity: Landau-Ginzburg phenomenological theory Free energy F P Order parameter (polarization) = ap + bp + cp +... EP F = 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 χ = P 1 = E a Assuming linear dependence of a on temperature we will have: α = 1 C ( T T c ) and finally we will have Curie-Weiss law χ = C ( T Tc ) 4/12/211 Physics 43 Spring 211 1

11 Ferroelectricity: Landau-Ginzburg phenomenological theory 8 In case of b>) (C> also) We will have the solution for second order phase transition with two equilibrium points p and p. Both these states are equivalent F (a.u.) E= T>T c T=T c T<T c P (a.u.) 4/12/211 Physics 43 Spring p p

12 Ferroelectricity: Landau-Ginzburg phenomenological theory 4 PLZST ceramics Ps 4 3 F (a.u.) Ps P (a.u.) P (μc/cm 2 ) Sn:Ti =.24:.11 Pr F (a.u.) P (a.u.) Ps F P Including EP term can illustrate the P-E hysteretic behavior = ap + bp + cp E DC (kv/cm) EP F (a.u.) /12/211 Physics 43 Spring P (a.u.) Pr

13 Ferroelectricity: Susceptibility P = ε χ E For ferroelectrics ε>>1 and ε χ D = ε E + P = ε E + ε χe = ε (1 + χ) E = ε εe 9 C=1.9*1 5 ; T CW =385.2K Curie-Weiss law: ε C = ( T ) + ε T CW ε'/ T (K) 4/12/211 Physics 43 Spring

14 Ferroelectricity: Typical ferroelectric materials KH 2 PO 4 E DC =1.2kV/cm Courtesy Max Candocia, P43 Spring 211 4/12/211 Physics 43 Spring

15 Ferroelectricity: Typical ferroelectric materials BaTiO 3 cubic rhombohedral orthorhombic tetragonal 4/12/211 Physics 43 Spring

16 Ferroelectricity: Typical ferroelectric materials T C (K) Ps (μc/cm 2 ) KDP type Perovskites KH 2 PO KD 2 PO RbH 2 PO BaTiO KNbO PbTiO >5 LiTiO LiNbO 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 4/12/211 Physics 43 Spring

17 Ferroelectricity: Relaxors - PMN Pb(Mg 1/3 1/3 Nb 2/3 )O )O 3 ε'/ /ε' T (K) Temperature dependencies of the real part of the dielectric constant measured in a broad frequency range: 3* Hz [1,2] E.V. Colla et all., J. Phys.: Cond. Matter, 4,3671, (1992) 2. E.V. Colla et all. J. Appl. Phys., 83, 3298, (1998) ε'/ K 22K 25K 24K f (Hz) Frequency dispersion of e at different temperatures 4/12/211 Physics 43 Spring

18 Ferroelectricity: Solid solution relaxor-regular regular ferroelectric. (PMN).7 (PT).3 Paraelectric (cubic) T c (K) 5 Literature data single crystals ceramics 4 3 (PMN) (1-x) (PT) (x) phase diagram PT: PbTiO 3, ferroelectric with Curie temperature = 763K Regular ferroelectric (tetragonal) (PMN).6 (PT) (PMN).9 (PT).1 (PMN).7 (PT).3 x Relaxor state (pseudocubic) 4/12/211 Physics 43 Spring

19 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 Rochelle salt (3C) Barium titanate ceramic Lead zirconate titanate PZT 45/55 PMN-PT (sc) PZN-PT (sc) Piezoelectric properties of different materials 4/12/211 Physics 43 Spring