2. What`s a ferroelectric crystal ?
A ferroelectric crystal exibits an electric dipole moment even in
the absence of an external electric field.
Why ?
In the ferroelectric state, the center of positive charge of the
crystal does not coincide with the center of the negative charge.
Ferroelectricity in such crystals appears above a certain
temperature (transition temperature) and disappears above a
specific temperature (Curie temperature).
Tt < Tferroelectric < TC (paraelectric)
(pyroelectric)
3. Characteristics of ferroelectric crystals
Ferroelectric materials exhibit hysteresis properties similar to
ferromagnetic materials...
that means...
in ferroelelctric materials exist domains...
but the crystal as a whole is un polarised
The presence of an external electric field
with altering intensity...
makes the domains change size and shape
E
(polarisation)
4. 1943 were discovered the ferroelectric properties of BaTiO3
Ferroelectric properties are determined by the behavior of the
central ion Ti
193 – 273 K orthorhombic system, Ti4+ is displaced toward
the diagonal of the elementary cell wall [110].
183 K there is a phase trasition: ferroelectric orthorhombic
phase – ferroelectric rhombohedral phase.
278 K there is a phase transition: ferroelectric orthorhombic
phase – ferroelectric tetragonal phase (278 – 393).
393 K phase transition: ferroelectric tetragonal – ferroelectric
Pseudocubic (regular structure).
Properties of BaTiO3
5. cubic tetragonal orthorhombic
Structural Modifications of BaTiO3 and their Characteristics
Pm-3m P4mm Amm2
a = 4.0000 Å a = 3.9945 Å
c = 4.0335 Å
a = 3.9900 Å
b = 5.6690 Å
c = 5.6820 Å
Ba – O
2.828 Å
Ti – O
2.000 Å
Ba – O
2.826 – 2.838 Å
Ti – O
1.863 – 2.170 Å
Ba – O
2.784 – 2.898 Å
Ti – O
1.929 – 2.090 Å
6. hexagonal trigonal
Structural Modifications of BaTiO3 and their Characteristics
P63/mmc R3m
a = 5.7350 Å
c = 14.0500 Å
a = 3.0010 Å
α = 89.85 °
Ba – O
2.852 – 2.956 Å
Ti – O
1.948 – 2.015 Å
Ba – O
2.771 – 2.896 Å
Ti – O
1.881 – 2.129 Å
7. What causes the ferroelectricity in such crystals ?
Oxygen – vacancy defects
Cubic phase PbTiO3
8 neighboring oxigens move toward the defect about 0.14 Å
4 neighboring lead atoms move toward the defect about 0.07 Å
2 vacancy – closest Ti atoms move outward the defect about 0.17 Å
Atom
Charge
Perfect crystal With vacancy Displacement
Ti(1)
Ti(2)
O(3)
O(4)
O(5)
O(6)
O(7)
O(8)
O(9)
O(10)
Pb(11)
Pb(12)
Pb(13)
Pb(14)
2.48 2.38
2.48 2.38
-1.39 -1.38
-1.39 -1.38
-1.39 -1.38
-1.39 -1.38
-1.39 -1.38
-1.39 -1.38
-1.39 -1.38
-1.39 -1.38
1.70 1.71
1.70 1.71
1.70 1.71
1.70 1.71
0.17
0.17
0.14
0.14
0.14
0.14
0.14
0.14
0.14
0.14
0.07
0.07
0.07
0.07
Relax. Energy (init.-optim.) = 11.5 eV
8. Tetragonal phase PbTiO3
Oxygen – vacancy defects
Atom
Charge
Perfect crystal With vacancy
Displacement
xy z total
Ti(1)
Ti(2)
O(3)
O(4)
O(5)
O(6)
O(7)
O(8)
O(9)
O(10)
Pb(11)
Pb(12)
Pb(13)
Pb(14)
2.37 2.26
2.40 2.29
-1.32 -1.30
-1.32 -1.30
-1.32 -1.30
-1.32 -1.30
-1.38 -1.36
-1.38 -1.36
-1.38 -1.36
-1.38 -1.36
1.74 1.69
1.74 1.69
1.74 1.69
1.74 1.69
0.00 0.53 0.53
0.00 0.06 0.06
0.12 0.18 0.21
0.12 0.18 0.21
0.12 0.18 0.21
0.12 0.18 0.21
0.08 0.24 0.25
0.08 0.24 0.25
0.08 0.24 0.25
0.08 0.24 0.25
0.03 0.00 0.03
0.03 0.00 0.03
0.03 0.00 0.03
0.03 0.00 0.03
Ferroelectricity due to the dipole
moment along z - axis
z
4 upper neighboring oxigens move toward the vacancy
4 neighboring lead atoms move outward the vacancy
2 vacancy – closest Ti atoms move outward the vacancy
4 lower neighboring oxigens move outward the vacancy
Relax. Energy
(init.-optim.) = 5.1 eV
9. The influence of the dopant (La) in the cubic phase
The relaxation of the lattice shows these movements:
Ti moves outward the defect(La) by 0.07 Å along <111>
O moves toward the defect by 0.02 Å along z – axis
(studied by means of advanced quantum-chemical method based on Hartree-Fock theory)
10. What happens with the extra e
incoming with La ?
Asymetric lattice distortion
Localized in local energy level
Charge distribution along z
z
Asymetric distortion of the cubic lattice
2 – Localization within the band gap
No increasement of electrical conductivity
(electrical dipole)
La in the cubic phase facilitates the phase transition (tetragonal)
Relaxation energy = 0.94 eV
(Coloumb destabilizing forces)
12. Hexagonal BaTiO3
Two zone – centre structural
phase transitions:
P63/mmc
Non-polar C2221
222 K
74 K ferroelectric P21phase
The same distortions of the TiO6 octahedra as in c-BT are observed
Similar chains of dipoles
13. Is there any change of ferroelectricity related
to particle size ?
Variation of permittivity for
presintered samples obtained from
Powder of different - sized
A, ∅ < 1.3μm
B, 1.3 < ∅ < 6.6 μm
C, 6.6 < ∅ < 18 μm
D, 18 < ∅ < 26 μm
E, 26 < ∅ < 50 μm
∅(particle) = f (temperature, sintering period)
No ∅ changes are observed for 1 hour at 1200°C
∅ of different particles is checked with microscope
spherical (1.3 < ∅ < 6.6 mm)
Influence of the form of the particles
cubic particles (1 mm)
The permittivity of the particles resulted:
spherical 202 cubic 215
Permittivity depends strongly on the way of
preparation and treatment of the materials
Studies on ferroelectricity in small coloidal
dots of BaTiO3 (0.5 nm) showed the presence
of large off-center displacements.
14. Efects of the additives on the properties of
BaTiO3 ceramics
Composition
ρB
(gcm-3)
TC
(°C)
Lattice
a (Å)
Constants
c (Å)
Ratio
c/a
BaTiO3
(BaTiO3)99.95(CeO2)0.05
(BaTiO3)99.5(CeO2)0.5
(BaTiO3)99(CeO2)1
(BaTiO3)98.5(CeO2)1.5
(BaTiO3)98(CeO2)2
(BaTiO3)97(CeO2)3
(BaTiO3)94.4(CeO2)5.6
(BaTiO3)93.8(CeO2)16.2
5.42
5.46
5.58
5.70
5.74
5.76
5.80
5.86
5.91
106
103
102.5
101.5
100.5
92
92
Smeared
Smeared
3.9965
3.9994
3.9962
3.9985
3.9958
4.0007
4.0008
4.0033
4.0112
4.0328
4.0358
4.0351
4.0310
4.0239
4.0130
4.0088
4.0083
3.9885
1.009083
1.009101
1.009734
1.008128
1.007032
1.003074
1.001999
1.001249
0.994341
A large number of dopands can be accommodated in the lattice of perovskites due to its
capability to host ions of different size causing substitution of Ba2+ or Ti4+, like: Pb2+,
Bi3+, Cu2+, Ca2+, Si4+, La3+, Ce2+, La2O3, CeO2
tetragonal – cubic – tetragonal (reverse direction)
15. Variation of permittivity (ε)
with temperature (T) °C
Variation of bulk density (ρB)
with CeO2 concentration
Variation of with CeO2 concentration
Variation of permittivity, bulk density and Curie
temperature for CeO2 doped BaTiO3(tetragonal) samples
(A): 0.05 mol% CeO2
(B): 0.5
(C): 1.0
(D): 1.5
(E): 2.0
(F): 3.0
(G): 5.6
(H): 16.2
16. 1
2
Tetragonal BaTiO3
Cubic BaTiO3
Formation of a solid solution from CeO2 doping BaTiO3
Two possible substitutions occur in the structure of BaTiO3
Ionic radii: Ce4+, Ti4+, O2-
1.01Å 0.68 Å 1.32 Å
Increasing the Ce4+ concentration conversion of the lattice from
tetragonal-cubic takes place decreasing the magnitude of spontaneous
polarisation, thus the permittivity.
17. Some preparation methods for ferroelectrics
Pulsed laser deposition
Thermal decomposition
Thin films by Sol – gel process
Patterned microstructures by sol-electrodeposition
Solid state reactions
Polymer composite films
Hydrothermal epitaxial thin films formed on epitaxial
electrode
18. Solid – state preparation method
BaCO3 + TiO2 = BaTiO3 + CO2
BaCO3 and TiO2 are mixed well in agate mortar
The mixture was heated at 1300°C – 6 h in air
Ball milled
Addition of additives
(BaTiO3)1-x + (CeO2)x
CuO - (BaTiO3)1-x + (AgNO3)x
Mixture was pressed in pellets and sintered at certain temperatures
0.05 -16.2 % mol
1 - 6 % mol
Measurements of the respective permittivities
19. Thermal decomposition as a preparation method
This method is applied to produce nm-sized BaTiO3 crystalites
Two steps thermal treatment of BaTiO(C2O4) x 2 H2O
1- treatment at 400°C for 1h under O2 flow
BaTiO(C2O4) x 2 H2O + O2 → BaTiO3 + CO2 + H2O
2- treatment of formed BaTiO3 at various temperatures in vacuum
Average particle size analyzed by (TEM), impurities by (FT-IR)
BaTiO3 crystalites with an average size of 16.5 nm were obtained
Dielectric constat (BaTiO3 16.5nm) resulted almost 400
20. Ferroelectric ceramic – polymer composite films
Purpose: Production of ferroelectric ceramic – polymer composite
films with high dielectric constant (ε) for high frequency electronics
Materials: BaTiO3 filler as the best known ferroelectric ceramics
Trimethylolpropan triacrylate (TMPTA monomer)
2,2 – dimethoxy – 2 – phenylacetophenone (photoinciator)
1- 1% solution of the photoinitiator was mixed with the main solution
2- BaTiO3 was mixed with TMPTA at various filler concentrations (main sol.)
3- Each solution was mixed with the photoinitiator
4- Few drops of each formulation were squezed between microscope slides
and exposed to UV -light
5- The thin flims prepared were examined with laser scanning confocal
microscopy
6- Dielectric measurements Impedance/Gain analyser, at 25°C, 1kHz
22. Dependence of cluster size and dielectric constant
from the volume fraction of BaTiO3 particles
The non – uniformity of the particle distribution caused by cluster formation
doesn`t affect macroscopic dielectric properties of BaTiO3 – polymer composites
23. Hydrothermal epitaxial thin films formed
on epitaxial electrode
BaTiO3 pseudocubic epitaxial thin films formed on epitaxial
electrode layers of SrRuO3 on SrTiO3 single crystal substrates
TiO2powder + Ba(OH)2(aq) → BaTiO3(H2O,OH-, CO3
2-)
90°C
pH = 14
Reaction time = 24 h
Product washed and recovered CO2 - free water
SrRuO3-SrTiO3 single-crystal was placed in the bottle before adding TiO2 powder
where SrRuO3 serves as electrode film and SrTiO3 as substrate for the over growing BaTiO3
The thin film obtained was pseudocubic and grown in the same
orientation as SrRuO3 and SrTiO3
24. XRD analyses showed the lattice constants for: BaTiO3, SrRuO3, SrTiO3
4.018 Å 4.037 Å 3.905 Å
Bright-field cross-section TEM micrograph
of the BaTiO3/SrRuO3/SrTiO3 film
SEM micrograph of the BaTiO3 thin film
grown on SrRuO3/SrTiO3 substrate
a) XRD pattern of BaTiO3/SrRuO3/SrTiO3
b) off-axis Φ-scans of (310) reflection of
BaTiO3 thin film, (220) of SrRuO3 buffer
layer and (220) reflection of SrTiO3
25. Preliminary investigations on epitaxial BaTiO3/SrRuO3 thin films show:
Before heat-treatment high losses of (ε ~ 450, δ ~100 %)
After heat-treatment (300 °C) low losses are observed (ε ~ 200, δ ~ 8 %)
To improve the electrical properties heating treatment of the film is suggested
1- T = 30 to 250°C 0.4 wt.% due to surface water and OH-
2- T = 250 to 800 °C 1.1 wt.% due to lattice H2O and OH-
3- T = 800 to 900 °C 0.25 wt.% due to CO2 evolution
Dielectric constant vs frequency as a
function of heat treatment for 1h.
Dielectric constant vs frequency as a
function of heat treatment at 300°C
26. Net weight loss as a function of
heat-treatment for 1h
TGA plot of BaTiO3 heated from
RT to 900°C at 2°C/min
OH- incorporation within the lattice is inevitable in hydrothermal
synthesized materials
1- Heating from RT to 300°C shows a decrease in lattice parameters
2- after 800 °C lattice begins to convert in tetragonal phase
3- over 1000 °C the films become fully tetragonal
Location of water within the crystal lattice: a) highly defective shell
b)BaCO3/BaTiO3 interfaces
27. Applications of titanates
BaTiO3, SrTiO3, PbTiO3 because of high dielectric constants
At room temperature and piezoelectric properties find
Applications in electronics.
Capacitors
Piezoelectric tranducers
Thermistors
Actuators
(large electro – optic coefficients and high photorefractive sensitivity)
Sensors
28. The stored charge Q in a capacitor is
proportional with the applied voltage U
Q ~ U
The proportional factor is the capacitance C
Q = CU
C = ε0 x εr x A/d ε0 = absolute dielectric constant (absolute permittivity)
εr = relative dielectric constant (relative permittivity)
(depends on insulation material)
A = plate surface in cm2
d = distance between plates in cm
The capacitor and application of permittivity
C = capacitance in F
29. Applications
Characteristics of Ag doped CuO-BaTiO3 CO2 Sensor
Ag doped CuO-BaTiO3 is a sensor that detects CCO2 in air from 100 ppm – 10 %
Ag increases the absorption of CO2 on the surface (catalyst)
Ag absorbs CO2 molecules to produce Ag2CO3
How does the doping ratio influence the sensitivity ?
30. Influence of the annealing
Ag doped CuO-BaTiO3 is a sensor is significantly affected by
sintering temperature
Sintering time 4h, CCO2 = 5000 ppm
31. Literature
1.- Randall, J. Am. Cheram. Soc., 81 (1998) p. 979
2.- M.R. Srinivasan, M.S.Multani, P. Ayyub, R. Vuayaraghavan, Ferroelectrics,
51 (1983) p. 137
3.- J. C. Cousseins, Phys. Stat. Sol. (a), 160 (1997), p. 255
4.- Z. Jiao, F. Chen, Sensors 2 (2002), p. 366-373
5.- J. C. Bourdreaux, R. H. Dauskardt, Mat. Res. Society 9 (2001) p. 1-6
6.- A. T. Chien, X. Xu, J. H. Kim, J. S. Speck, J. Mater. Res. Vol. 14, 8 (1999) p. 3330-3339
7.- H. Pinto, A. Stashans, P. Sanchez, Cendro de Investigation en Fisica de la Materia
Condensada. Corporacion de Fisica Fundamental y Aplicada. Apartado 17-12.637,
Quito Ecuador
8.- Edgar Patino, Arvidis Stashans, Cendro de Investigation en Fisica de la Materia
Condensada. Corporacion de Fisica Fundamental y Aplicada. Apartado 17-12.637,
Quito Ecuador
9.- Sheyla Serrano, Carlos Duque, Paul Medina, Arvids Stashans, Cendro de
Investigation en Fisica de la Materia Condensada. Corporacion de Fisica
Fundamental y Aplicada. Apartado 17-12.637, Quito Ecuador
10.- H. Fu, L. Bellaiche, J. Phys. Rev, Letters Vol. 91, 25 (2003) p. 1-4
11.- J. Paletto, G. Grange, R. Goutte, L. Eyraud, J. Appl. Phys. Vol 7 (1974)
p. 78-84
12.- M AA Issa, N M Molokhia, Z H Dughaish J. Appl. Phys. Vol. 16 (1983)
p. 1109-1114
