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
Mediterranean School on NanoPhysics Marrakech, 2 11 December 2010 Ferroelectrics: Theoretical Concepts and Applications Hamadi KHEMAKHEM Ferroelectric Material Laboratory Faculty of Sciences of SfaxTunisia
Plan du cours! Dielectric Materials! Local Field! Dielectric Relaxation! Ferroelectric Materials! Landau Theory! Applications
Dielectric Materials!! Definition of permittivity!! Complex representation
Dielectric Materials! 2" Z! 1 Z "
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
Dielectric Materials
Local Field c a! E ext
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 = 1 0 0 1 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
Local Field Determination of E2
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
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
Dielectric Relaxation
Dielectric Relaxation ColeCole Diagram! 2! f increases! $=1/%"! 1! Cours 1 Généralités
Dielectric Relaxation Real part of permittivity 2.5 10 4 Gold 8.18/3.17 300K Silver paste 9.21/3.08 300K In/Ga 9.21/2.85 298K electrod 2 10 4 1.5 10 4 1 10 4 5000 0 100 1000 10 4 10 5 10 6 10 7 10 8 f(hz)
Dielectric Relaxation Imaginary part Effet de la température et de la conductivité
Dielectric Relaxation Relaxation and resonance
Ferroelectric Materials 32 crystal classes 11 centrosymetric 21 non centrosymetric non piezoelectric 20 piézoélectriques piezoelectrics 1 non piezoelectric 10 10 pyroélectriques pyroelectrics 10 non pyroelectrics non ferroelectrics ferroélectriques ferroelectrics Non ferroelectrics
Ferroelectric Materials P s : polarisation à saturation E c : champ coercitif P r : polarisation rémanente Hysteresis Loop
Ferroelectric Materials!!! r 12000! 10000! 8000! 6000! Ferroelectric Paraelectric! 4000! 2000! 0! 300! 400! 500! 600! 700! 800! T C T ( C)!
Pyroelectric parameter Le courant de polarisation est proportionnel à la vitesse de changement de température et au signe de variation
Impedance of a circuit R, C parallel if R and C are independent of frequency, we write Z = Z'jz R! C! at the top of the semicircle we have: RC= 1/$! Z! R = extrapolation to zero frequency of Z '(when (Z'') vanishes)! Z! When the frequency tends towards infinity (Z'') vanishes! Cours 1 Généralités
Landau Theory Landau Model for ferroelectricparaelectric phase transition
Landau Theory Curie Weiss law
Landau Theory Curie Weiss law
Landau Theory Free energy : Second order transition T>T C T=T C T<T C
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
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 E3 0 50 0 50 100 150 T ( C)
Applications Classic Ferroelectric! ' r Polar Non polar T C and! r does not vary with frequency! no dispersion 0 T C 0 100 200 300 400 T (K)
Applications Relaxor! r 25000 20000 15000 * Dispesion in ferroelectric state * Variation of Tm with frequency 10000 5000 0 50 100 150 200 250 300 350 400 &T m T (K)
Applications Relaxor Local fluctuation of composition in the A site caused by the substitution!" Nanometric areas T 1 T m T i T