Mediterranean School on Nano-Physics held in Marrakech - MOROCCO December Ferroelectrics: Theoretical Concepts and Applications

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1 22182 Mediterranean School on NanoPhysics held in Marrakech MOROCCO 2 11 December 2010 Ferroelectrics: Theoretical Concepts and Applications KHEMAKHEM Hamadi Faculte des Sciences de Sfax Departement de Physique Laboratoire des Materiaux Ferroelectriques Route de Soukra km 3,5 B.P. 1171, 3000 Sfax TUNISIA

2 Mediterranean School on NanoPhysics Marrakech, 2 11 December 2010 Ferroelectrics: Theoretical Concepts and Applications Hamadi KHEMAKHEM Ferroelectric Material Laboratory Faculty of Sciences of SfaxTunisia

3 Plan du cours! Dielectric Materials! Local Field! Dielectric Relaxation! Ferroelectric Materials! Landau Theory! Applications

4 Dielectric Materials!! Definition of permittivity!! Complex representation

5 Dielectric Materials! 2" Z! 1 Z "

6 Dielectric Materials Electronic Polarization : P e Atomic or ionic polarization: P a P = P e P a P d P c Dipolar polarization: P d Space charge polarization : P C

7 Dielectric Materials

8 Local Field c a! E ext

9 Local Field Determination of E1 Materials that have an ellipsoidal shape have an important property: When the field is uniform, the polarization is uniform.!polarization is related to the field by the depolarization factor N: Facteur de dépolarisation 1 Nx Ny Nz = c/a Rq: Nx, Ny et Nz are the depolariztion factors, their values depend on the relationship between the For a sphere Nx=Ny=Nz = 1/3 principal axes of the ellipsoid. 1/3

10 Local Field Determination of E2

11 Local Field Determination of E3 Field E3, due to the dipoles inside the cavity is the only term that depond of the crystal structure. It has been shown that for a reference site with a cubic environment into a sphere, that:!e3 = 0

12 Local Field Clausius Mossotti law The polarization is expressed in terms of local field by : P = N#E loc : which is the microscopic representation #!: is the polarizability of material In the case of a material with several kind of atom j, the polarization is written: Catastrophe de Mossotti

13 Dielectric Relaxation

14 Dielectric Relaxation ColeCole Diagram! 2! f increases! $=1/%"! 1! Cours 1 Généralités

15 Dielectric Relaxation Real part of permittivity Gold 8.18/ K Silver paste 9.21/ K In/Ga 9.21/ K electrod f(hz)

16 Dielectric Relaxation Imaginary part Effet de la température et de la conductivité

17 Dielectric Relaxation Relaxation and resonance

18 Ferroelectric Materials 32 crystal classes 11 centrosymetric 21 non centrosymetric non piezoelectric 20 piézoélectriques piezoelectrics 1 non piezoelectric pyroélectriques pyroelectrics 10 non pyroelectrics non ferroelectrics ferroélectriques ferroelectrics Non ferroelectrics

19 Ferroelectric Materials P s : polarisation à saturation E c : champ coercitif P r : polarisation rémanente Hysteresis Loop

20 Ferroelectric Materials!!! r 12000! 10000! 8000! 6000! Ferroelectric Paraelectric! 4000! 2000! 0! 300! 400! 500! 600! 700! 800! T C T ( C)!

21 Pyroelectric parameter Le courant de polarisation est proportionnel à la vitesse de changement de température et au signe de variation

22 Impedance of a circuit R, C parallel if R and C are independent of frequency, we write Z = Z'jz R! C! at the top of the semicircle we have: RC= 1/$! Z! R = extrapolation to zero frequency of Z '(when (Z'') vanishes)! Z! When the frequency tends towards infinity (Z'') vanishes! Cours 1 Généralités

23 Landau Theory Landau Model for ferroelectricparaelectric phase transition

24 Landau Theory Curie Weiss law

25 Landau Theory Curie Weiss law

26 Landau Theory Free energy : Second order transition T>T C T=T C T<T C

27 Landau Theory Variation of permittivity and polarization 1/! r Transition de premier ordre Transition de second ordre 1/! r P s P s T 0 T c T T c =T 0 T

28 Applications Perovskite structure (ABO3): BaTiO3 O 2 O 2 T < Tc : P4mm 1 E4 8 E3 rhom. orth. 400 K ferro para quadr. cub. T > T C: Pm3m! r 6 E3 4 E3 2 E T ( C)

29 Applications Classic Ferroelectric! ' r Polar Non polar T C and! r does not vary with frequency! no dispersion 0 T C T (K)

30 Applications Relaxor! r * Dispesion in ferroelectric state * Variation of Tm with frequency &T m T (K)

31 Applications Relaxor Local fluctuation of composition in the A site caused by the substitution!" Nanometric areas T 1 T m T i T

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