ferroelectricity - tu graz
TRANSCRIPT
![Page 1: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/1.jpg)
Ferroelectricity
![Page 2: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/2.jpg)
ABX3
Ferroelectricity
Perovskites
Spontaneous polarizationAnalogous to ferromagnetismStructural phase transitionTc is transition temperature
Electric field inside the material,is not conducting
![Page 3: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/3.jpg)
Ferroelectric domains
Increasing the electric field polarizes the material.
![Page 4: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/4.jpg)
BaTiO3
cubic (contains i = > no spontaneous P)
Can be used to make nonvolatile memory
![Page 5: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/5.jpg)
BaTiO3
Can be used to make ultracapacitors
1r
+++ +++
- - - - - -
![Page 6: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/6.jpg)
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
![Page 7: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/7.jpg)
PbTiO3
Pyroelectric constant
Dielectric constant
Specific heat
1
cT T
Polarization
![Page 8: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/8.jpg)
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
![Page 9: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/9.jpg)
T > Tc T < Tc
Applied fieldT < Tc
![Page 10: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/10.jpg)
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.
![Page 11: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/11.jpg)
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
![Page 12: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/12.jpg)
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.
![Page 13: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/13.jpg)
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
![Page 14: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/14.jpg)
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
![Page 15: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/15.jpg)
Institute of Solid State PhysicsTechnische Universität Graz
Landau Theory of Phase Transitions
![Page 16: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/16.jpg)
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
![Page 17: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/17.jpg)
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
![Page 18: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/18.jpg)
Landau theory of phase transitions
0 cc
T Tm T T
![Page 19: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/19.jpg)
Free energy
2 410 0 2cf f T T m m
0 cc
T Tm T T
220
0cT T
f f
![Page 20: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/20.jpg)
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
![Page 21: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/21.jpg)
1st order 2nd order
![Page 22: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/22.jpg)
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
![Page 23: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/23.jpg)
Introduction to Superconductivity, Tinkham
![Page 24: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/24.jpg)
Specific heat
normal
superconducting
![Page 25: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/25.jpg)
Specific heat
![Page 26: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/26.jpg)
Fe
Specific heat
HePbTiO3
CuZn alloy -brassorder - disorder
![Page 27: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/27.jpg)
![Page 28: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/28.jpg)
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
![Page 29: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/29.jpg)
![Page 30: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/30.jpg)
Landau theory of phase transitions
LiTaO3
Curie-Weiss law
1r 0
1 2 cT T
![Page 31: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/31.jpg)
Fitting the and parameters
0
1 2 cT T
202 c
vTc
![Page 32: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/32.jpg)
Landau theory of phase transitions
0 cc
T Tm T T
0
can be determined from the temperature dependence of the order parameter
![Page 33: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/33.jpg)
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
![Page 34: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/34.jpg)
First order transitions
BaTiO3
![Page 35: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/35.jpg)
Tc?
Tc T1Tc
![Page 36: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/36.jpg)
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.
![Page 37: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/37.jpg)
Jump in the order parameter
At Tc
202 4
2cT T
m
m
At T1
2m
![Page 38: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/38.jpg)
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
![Page 39: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/39.jpg)
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,
![Page 40: Ferroelectricity - TU Graz](https://reader030.vdocuments.mx/reader030/viewer/2022012705/61a72034992f72019a7bd691/html5/thumbnails/40.jpg)