Principles of Ferroelectricity

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Intro to ferroelectrics

  • Possess spontaneous polarisation, altered by E-field
  • electric insulators
  • more than 1 stable state
  • Jahn-Teller effect: metal cations favour distorted bonding arrangement to surrounding Oxygen ions
  • Measure phase transformations through capacitance /permittivity lattice parameter (x-ray diffraction)
  • Crystal symmetry dictates in which direction polarisation occurs
  • Cp - T graph: after Tc, follows Curie Weiss law (dielectric permittvity is inversly proportional to temperature)

Tetragonal PZT domain walls

  • 180 degrees lie along (100) or (010)
  • 90 degrees lie along (101) or (011)
    • region around domain = distorted , a region of 'cubic state', with some strain energy
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Domain formation, Strain Hysteresis, Gibbs Free en

Domain formation

  • driven by elastic strain energy due to constrained transformation through Tc [Polycrystal]
  • minimise Gibbs free energy [Single crystal]

Strain field Hysteresis: Butterfly loop - symmetric

Gibbs free energy

  • Cubic state, minima at P=0 
  • ferroelectric, 2 non zero minima --> there is a spontaneous polarisation
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Landeau Theory: 1st and second order

Assumes order parameter vares as a function of temperature

2nd order

  • G-P: T>T0 --> single minima 
  • T=T0 --> flat region
  • T< T0 --> twin minima 
  • P-T gradual reduction of P
  • Dielectric susceptibility: curie weiss, 1/x is linear

1st order

  • G-P: T> Tc: local minmima , meta-stable polarisation state
  • T= Tc : 3 minima
  • T =T0< Tc: 2 minima
  • P-T--> drops discontinuously at curie tempererature
  • Dielectric susceptibility: peak, Curie Weiss
  • G predicts values greater than measured due to domain wall and lattice defects effects
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Simple and Complex perovskites

  • Stability of polarisation chnages as E-field is applied
  • Gibbs -P curve can predict switching and hysteresis loop

Tolerance factor: Measure stability of crystal, compare to ideal lattice parameters

Perovskites

  • Sum of cation charges = 6+
  • isovalent --> same oxidation state , aliovalent : different state oxidation state

Complex perovskite

  • different oxidation state ions on single site
  • not stable over wide range of composition
  • disorder on sites affects properties
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Relaxor Ferroelectrics

  • broad permittivity- T peak, at Tm instead of Tc 
  • frequency dependence on permittivity and temperature
  • pseudocubic transformation at Tm
  • gradual change to rhombohedral or teragonal at ~100 degrees celsius below Tm
  • Origin
    • disorder on sites = different polarisation abilities at sites
    • nanoscale compositional flunctuations 
    • unstable polar regions
  • At low temperatrue, polar regions more stable and larger ,
  • T~ 100 degrees celsius, below Tm get convential domains (below)
  • For T~Tm , get electrostrictive behaviour
  • Electrostrictive --> quadratic relation between strain and E-field
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Comparison of Relaxor Ferroelectrics

  • no Tc, low T; long range domains
  • Td: depolarisation , slim loop, low remnant --> becomes linear
  • Tb: conformation to curie weiss law
  • Paraelectric: no domains
  • Relaxor phase  < Tb: nanodomains , flunctuation in size
  • Then coexistence of static and dynamic domains
  • Frozen phase: static and polarisable domains
  • Electrostrictive --> x proportional P2
  • Piezoelectric effect: biased electrostriction by spontaneous polarisation
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