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Ferroelectricity
ABX3
Ferroelectricity
Perovskites
Spontaneous polarizationAnalogous to ferromagnetismStructural phase transitionTc is transition temperature
Electric field inside the material,is not conducting
Ferroelectric domains
Increasing the electric field polarizes the material.
BaTiO3
cubic (contains i = > no spontaneous P)
Can be used to make nonvolatile memory
BaTiO3
Can be used to make ultracapacitors
1r
+++ +++
- - - - - -
Ferroelectric
Paraelectric state
Above Tc, BaTiO3 is paraelectric. The susceptibility (and dielectric constant) diverge like a Curie-Weiss law.
1
cT T
This causes a big peak in the dielectric constant at Tc.
01
Paraelectric
PbTiO3
Pyroelectric constant
Dielectric constant
Specific heat
1
cT T
Polarization
Antiferroelectricity
Polarization aligns antiparallel.
Associated with a structural phase transition.
Large susceptibility and dielectric constant near the transition.
Phase transition is observed in the specific heat, x-ray diffraction.
PbZrO3
T > Tc T < Tc
Applied fieldT < Tc
Piezoelectricity
lead zirconate titanate (Pb[ZrxTi1−x]O3 0<x<1)—more commonly known as PZT
barium titanate (BaTiO3) Tc = 408 Klead titanate (PbTiO3) Tc = 765 Kpotassium niobate (KNbO3) Tc = 708 Klithium niobate (LiNbO3) Tc = 1480 Klithium tantalate (LiTaO3) Tc = 938 K
quartz (SiO2), GaAs, GaNGallium Orthophosphate (GaPO4) Tc = 970 K
Piezoelectric crystal classes: 1, 2, m, 222, mm2, 4, -4, 422, 4mm, -42m, 3, 32, 3m, 6, -6, 622, 6mm, -62m, 23, -43m
Third rank tensor, No inversion symmetry
Many ferroelectrics are piezoelectric.
Electric field couples to polarization, polarization couples to structure.
Piezoelectricity
When you apply a voltage across certain crystals, they get longer.
AFM's, STM'sQuartz crystal oscillatorsSurface acoustic wave generatorsPressure sensors - EpcosFuel injectors - BoschInkjet printers
PZT (Pb[ZrxTi1−x]O3 0<x<1)A
ntife
rroe
lect
ric
Large piezoelectric response near the rhombohedral-tetragonal transition.Electric field induces a structural phase transition.
Nitinol
Ni Ti alloy
Shape memory: If it is bent below a certain transition temperature and then heated above that temperature,
it returns to its original shape.
Superelasticity: Just above the transition temperature, the material exhibits elasticity 10-30 times that of an
ordinary metal.
Martisite - Austinite
Phase change memory
Phase-change memory (PRAM) uses chalcogenide materials. These can be switched between a low resistance crystalline state and a high resistance amorphous state.
GeSbTe is melted by a laser in rewritable DVDs and by a current in PRAM.
nonvolatile
Institute of Solid State PhysicsTechnische Universität Graz
Landau Theory of Phase Transitions
Landau theory of phase transitions
A phase transition is associated with a broken symmetry.
magnetism direction of magnetizationcubic - tetragonal different point groupwater - ice translational symmetryferroelectric direction of polarizationsuperconductivity gauge symmetry Lev Landau
Temperature dependence of the order parameter
At T=Tc = 0
2 410 0 2cf f T T m m
The temperature dependence of the magnetization is
0 cc
T Tm T T
Expand interms of T - Tc. Keep only the linear term. m and T - Tc are both small near Tc.
minimize m
Landau theory of phase transitions
0 cc
T Tm T T
Free energy
2 410 0 2cf f T T m m
0 cc
T Tm T T
220
0cT T
f f
Entropy
220
0 ( ) cT Tf f T
20
0
2( ) cT Tfs s T
T
0c A BL T S S
This is a second order phase transition
Kink in the entropy
1st order 2nd order
Specific heat
20
0
2 cT Tfs s TT
Entropy
Specific heat 20
02 v c
Tsc T c T T TT
There is a jump in the specific heat at the phase transition and then a linear dependence after the jump.
202 c
vTc
Introduction to Superconductivity, Tinkham
Specific heat
normal
superconducting
Specific heat
Fe
Specific heat
HePbTiO3
CuZn alloy -brassorder - disorder
Landau theory, susceptibility
2 410 0 2cf f T T m m mB
Add a magnetic field
0
2 c
c
Bm T TT T
302 2 0c
df T T m m Bdm
Above Tc, m is finite for finite B. For small m,
0
1 2 cT T
Curie-Weiss
Landau theory of phase transitions
LiTaO3
Curie-Weiss law
1r 0
1 2 cT T
Fitting the and parameters
0
1 2 cT T
202 c
vTc
Landau theory of phase transitions
0 cc
T Tm T T
0
can be determined from the temperature dependence of the order parameter
First order transitions
There is a jump in the order parameter at the phase transition.
2 4 61 10 0 02 3 0, 0, 0cf f T T m m m
First order transitions
BaTiO3
Tc?
Tc T1Tc
First order transitions
There will be a minimum at finite m as long as m2 is real
2 4 61 10 0 2 3 0 0cf f T T m m m
3 502 2 2 0c
df T T m m mdm
202 4
0,2
cT Tm
2
104 cT T
2 40 0cT T m m
One solution for m = 0.
Jump in the order parameter
At Tc
202 4
2cT T
m
m
At T1
2m
First order transitions, entropy, cv
2004 ( )
2 cfs T TT
2 4 61 10 0 2 3 0cf f T T m m m
204
0,2
cT Tm
20
204 ( )
v
c
Tsc TT T T
branch where the order parameter is nonzero
First order transitions, susceptibility
At the minima
2 4 61 10 0 2 3 0cf f T T m m m mB
3 502 2 2 0c
df T T m m m Bdm
3 502 2 2cB T T m m m
0 0
12m c
dmdB T T
Curie - Weiss
0 12
12m
dmdB T T
For small m,