Ferroelectrics. Disordered Ferroelectrics...F P 6aP bP cP ... EP 6 1 4 1 2 1 2 4 Free energy Order...
Transcript of Ferroelectrics. Disordered Ferroelectrics...F P 6aP bP cP ... EP 6 1 4 1 2 1 2 4 Free energy Order...
![Page 1: Ferroelectrics. Disordered Ferroelectrics...F P 6aP bP cP ... EP 6 1 4 1 2 1 2 4 Free energy Order parameter (polarization) ... type KH 2 PO 4 123 4.75 KD 2 PO 4 213 4.83 RbH 2 PO](https://reader034.fdocuments.in/reader034/viewer/2022051906/5ff9350a58add434d0617599/html5/thumbnails/1.jpg)
Ferroelectrics. Disordered Ferroelectrics
1Physics 403 Spring 2020
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• Ferroelctricity
• Main properties
•History. Discovery. Materials
• Disordered Ferroelectrics Relaxors
• Applications
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• Ferroelectric Materials. A ferroelectric material
is a material that exhibits, over some range of
temperature, a spontaneous electric
polarization that can be reversed or reoriented
by application of an electric field.
3
An American National StandardIEEE Standard Definitions ofPrimary Ferroelectric Terms
Physics 403 Spring 2020
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Ferroelectricity: Two classes of ferroelectrics
Displacement type
N
O
O
Order-Disorder
disorder
order
NaNO2
Ba
Ti O
P
PBaTiO3
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-40 -30 -20 -10 0 10 20 30 40
-40
-30
-20
-10
0
10
20
30
40 Sn:Ti = 0.24:0.11
PLZST ceramics
P (C
/cm
2)
EDC
(kV/cm)
Ferroelectricity: Polarization reversible. (P-E hysteresis)
5Physics 403 Spring 2020
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Ferroelectricity: Domains
+
-
Pnet~0
Single domain state
Multi domain state
180o domain pattern
90o domains
Y Lu et al. Science 1997;276:2004-2006
Courtesy of Igor Lukyanchuk
http://www.lukyanc.net/stories/nano-worldofdomains
6Physics 403 Spring 2020
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Ferroelectricity: Domains
Courtesy of Benjamin Vega-Westhoff
and Scott Scharfenberg, P403, Fall2009
BaTiO3
BaTiO3
Crystal from Forschungsinstitutfür mineralische und metallische
Werkstoffe -Edelsteine/Edelmetalle
KH2PO4
Courtesy of Allison Pohl, P403,
Fall2009
KD2PO4191K
PMN-PT40%
PMN-PT30%
7Physics 403 Spring 2020
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Ferroelectricity: Landau-Ginzburgphenomenological theory
EPcPbPaPFP −+++= ...6
1
4
1
2
1 642
Free energyOrder parameter (polarization)
Electric fieldthe equilibrium solution 0=
P
F
Ignoring higher terms we can get the linear solution:
0F
aP EP
= − =
aE
P 1=
=
Assuming linear dependence of a on temperature we will have:
1( )
cT T
C = − and finally we will have Curie-Weiss law
( )c
C
T T =
−
Lev Landau1908-1968
Vitaly Ginzburg1916-2009
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-7 0 7
0
10
20
30
40
50
60
70
80
F (
a.u
.)
P (a.u.)
Ferroelectricity: Landau-Ginzburgphenomenological theory
In case of b>) (C>0 also) We will
have the solution for second
order phase transition with two
equilibrium points –p0 and p0.
Both these states are equivalent
T>Tc
T=Tc
T<Tc
E=0
p0
-p0
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-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-20
-10
0
10
20
30
40
F (
a.u
.)
P (a.u.)
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-20
-10
0
10
20
30
40
F (
a.u
.)
P (a.u.)
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12-20
-10
0
10
20
30
40
F (
a.u
.)
P (a.u.)
-40 -30 -20 -10 0 10 20 30 40
-40
-30
-20
-10
0
10
20
30
40 Sn:Ti = 0.24:0.11
PLZST ceramics
P (C
/cm
2)
EDC
(kV/cm)
Ferroelectricity: Landau-Ginzburgphenomenological theory
EPcPbPaPFP −+++= ...6
1
4
1
2
1 642
Including EP term can illustrate
the P-E hysteretic behavior
-PsPs
Pr
Pr
Ps
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400 450 5000
3
6
9
T (K)
'/1
00
0Ferroelectricity: Susceptibility
0P E = 0 0 0 0 0
(1 )D E P E E E E = + = + = + =
For ferroelectrics >>1 and ≈
Curie-Weiss law:
00)(
+−
=CWTT
C
C=1.9*105;
TC=385.2K
BaTiO3
11Physics 403 Spring 2020
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Rochelle Salt KNaC4H4O6*4H2O
Potassium sodium tartrate discovered (in about 1675) by an apothecary, Pierre Seignette
Elie Seignette
Rochelle Salt originates fromFrench city of La Rochellewhere it was produced byPierre Seignette anothername of this material isSeignette salt
Rochelle Salt was used
in medicine and food
industry
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Rochelle Salt KNaC4H4O6*4H2O
Paul-Jacques Curie1856 – 1941
Pierre Curie1859-1906
Brothers Curie discovered and investigated the piezoelectric effect I several materials including Rochelle salt
13Physics 403 Spring 2020
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Rochelle Salt KNaC4H4O6*4H2O
Joseph Valasek (1897-1993)
University of Minnesota
1920 1969
1. J. Valasek, Phys. Rev. 17, 475 (1921)
2. J. Valasek, Phys. Rev. 19, 478 (1922)
Fig.1. The first published
hysteresis loop [1]Fig3. Piezoelectric
response as a function
of temperature [2]
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Ferroelectricity. Terminology.
ferrum (Lat) gave the name of the broad class of magnetic materials – ferromagnetics
Fe has no relation to the phenomenon of ferroelctricity but
because of a lot of common features of ferroelectric phase transition to ferromagnetic the “new” class of dielectrics was named as ferroelectrics.
There is another name for this class of materials - Seignette-electrics named after the alternative name of the Rochelle salt
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KDP (KH2PO4) - potassium dihidrophosphate
G. Busch and P. Scherrer, Naturwiss. 23, 737 (1935). Eine neue Seignetteelektrische Substanz. 1935
Paul Scherrer1890-1969
Georg Busch 1908-2000
Tc ~123K
Physics 403 Spring 2020
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KDP (KH2PO4) - potassium dihidrophosphate Tc ~123K
100 150 200 2500
1
2
31000kHz
KDP (sample 4) c-cutheating
T (K)
'/1
00
0
KDP project (2): Graph6
Courtesy of Tim S. Thorp, Zhangji Zhao, Physics 403, Spring 2013
Tc~121.5 K
Courtesy of Alison Pohl, Physics 403, Spring 2009
T>Tc
T<Tc
Physics 403 Spring 2020
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DKDP (KD2PO4) – deuterated potassium dihidrophosphateTc ~230K
T>Tc
T<Tc
Physics 403 Spring 2020
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19
1943 – material with high (>1200) value of the dielectric constant (Wainer, Solomon (USA); Wul, Goldman (USSR))
Tc ~400K
1945 – discovered the ferroelectric properties of BaTiO3 A. von Hippel (USA); Wul, Goldman (USSR))
Arthur R. von Hippel1898-2003
A. Von Hippel, Rev. Mod. Phys. 22,221, 1950Physics 403 Spring 2020
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tetragonal
orthorhombic
rhombohedral
Walter J. Merz, Phys. Rev. 76, 1221, 1949
’P
(
C/c
m2)
P
P
P
Physics 403 Spring 2020
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21
John A. Hooton, Walter J. Merz, Phys. Rev. 98, 409,1955
Physics 403 Lab, August 2011
Physics 403 Spring 2020
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22
150 200 250 300 350 400 450 5000
3
6
9
cooling
heating
100Hz
T (K)
'/1
000
-20 -15 -10 -5 0 5 10 15 20
-30
-20
-10
0
10
20
30
345K
395K
P (
C/c
m2)
E (kV/cm)
395K345K
Courtesy of Liu M. & Lopez P, Physics 403, Spring 2013
Physics 403 Spring 2020
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Ferroelectricity: Typical ferroelectric materials
Number of publications concerning ferroelectricity. From
Jan Fousek “Joseph Valasek and the Discovery of
Ferroelectricity”
Springer Handbook of Condensed Matter and Materials Data
TC(K) Ps (C/cm2)
KDP
type KH2PO4 123 4.75
KD2PO4 213 4.83
RbH2PO4 147 5.6
Perovskites BaTiO3 408 26
KNbO3 708 30
PbTiO3 765 >50
LiTiO3 938 50
LiNbO3 1480 71
ABO3
23Physics 403 Spring 2020
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Perovskite Structure
AB1(1-x)B2xO3 A1(1-x)A2xBO3 A1(1-x)A2xB1(1-y)B2yO3 typical complex oxides with perovskite structure
Perovskite is a mineral CaTiO3. The mineral was discovered in the Ural Mountains
of Russia by Gustav Rose in 1839 and is named after Russian mineralogist Lev
Perovski.
Gustav Rose1798-1873
Lev Perovski1792-1856
24Physics 403 Spring 2020
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New Perovskite Materials - Relaxors
Smolenskii G.A.2
(1910 – 1986)L. Eric Cross1
(1923-2016)
B-site complex
Lead magnesium niobate(PMN)
PbMgl/3Nb2/303
Lead scandium tantalate(PST)
PbSc1/2Ta1/203
Lead zinc niobate (PZN) PbZnl/2Nb1/203
Lead indium niobate (PIN) PbIn1/2Nb1/203
A-site complex
Lead lanthanum titanate(PLT)
Pb1-xLaxTiO3
Both sites complex
Lead lanthanum zirconate titanate (PLZT)
Pb1−xLaxZryTi1−yO3
Potassium lead zinc niobate K1/3Pb2/3Zn2/9Nb7/903 1. Pennsylvania State University, USA2. A.F. Ioffe Institute, USSR
AB1(1-x)B2xO3 A1(1-x)A2xBO3 A1(1-x)A2xB1(1-y)B2yO3 typical complex oxides with perovskite structure
25Physics 403 Spring 2020
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Relaxors
Ba O Ti
Relaxor - PMN Pb(Mg1/3 Nb2/3)O3Regular ferroelectric BaTiO3
OPb Mg+2 or Nb+5
T > Tc (cubic) (cubic)
26Physics 403 Spring 2020
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Relaxors
Ba O Ti
Relaxor - PMN Pb(Mg1/3 Nb2/3)O3Regular ferroelectric BaTiO3
OPb Mg+2 or Nb+5
T < Tc (tetragonal) (cubic)
27Physics 403 Spring 2020
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Temperature dependencies of ’ measured in a
broad frequency range: 3mHz -1MHz
150 200 250 300 350 400 4500
7
14
21
28
35
T (K)
'/1
000
0.05
0.10
0.15
0.20
0.25
0.30
0.35
10
3/
'
3mHz
1MHz
’max and Tmax depend on the measuring frequency
’ does not follow Curie-Weiss law
28Physics 403 Spring 2020
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250 255 260 265 270 275 280 285 29010
-3
10-1
101
103
105
TVF
~212K
f ma
x (
Hz)
Tmax
(K)
0
max 0exp
VF
Ef f
T T
−=
−
29Physics 403 Spring 2020
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Figure 3.(a) ABO3perovskite structure. (b) Model for relaxor structure. PNR and COR represent the polar nano-region and chemically order region, respectively. (c) &(d) show two models of atom arrangement for COR. To maintain the electric neutrality, a Nb-rich layer is required for case (c).
PNR – polar nanodomainsCOR – chemically ordered regions
D. Fu, et all in "Advances in Ferroelectrics", ISBN 978-953-51-0885-6, November 19, 201230Physics 403 Spring 2020
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100 200 300 400
0
5000
10000
15000
20000
25000
30000
'
T (K)
Regular Ferroelectrics - Relaxors
PMN BaTiO3
31Physics 403 Spring 2020BTO courtesy of James Graessle
Same structure but different behavior
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Disorder in Regular Ferroelectrics
BaTiO3 Rhombohedral phase
32Physics 403 Spring 2020
150 200 250 300 350 400
5
10
15
20
25
'/1
00
0
100 Hz
20 kHz
100 120 140 160 180 200 2200.5
1.0
1.5
2.0
2.5
3.0
3.5
'/1
000
T (K)
100Hz
20 kHz
BTO courtesy of James Graessle
(111)E
PMN remains in cubic phasebut it is easy to move it inrhombohedral phase byapplication of the DC field in(111) direction
PMN
BaTiO3
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Disorder in Regular Ferroelectrics. KDP family
33Physics 403 Spring 2020
KH2PO4
KD2PO4
KDP - Tc ~ 120 K
Deuterated analog DKDP Tc~230K
80 100 120 140 160 180 2000
500
1000
T (K)
'
500m 1 20.0
0.5
1.0
KDP
BTO
T/Tc
'/
' ma
x BaTiO3
KH2PO4
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Disorder in Regular Ferroelectrics. KDP family
34Physics 403 Spring 2020
80 90 100 110 120 130 140 1500.0
0.5
1.0
T (K)
'/1
00
0
100 Hz
50 kHz
120 140 160 180 200 220 240 2600.0
0.5
1.0
T (K)
'/1
00
0
100 Hz
20 kHz
KD2PO4KH2PO4
Below Tc KDP and DKDP show wide (> 30 K)
plateau. This state is not equilibrium and has a
trend to decrease the susceptibility in time (aging)
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Disorder in Regular Ferroelectrics. KDP family
35Physics 403 Spring 2020
Aging depends on the concentration of deuterium
in (KH2PO4)(1-x)(KD2PO4)x composition
200 220 240 260 280 300
400
600
800
1000
1200
'
T (K)
cooling
aging
KD2PO4
0 50 100 150 200 250 300
400
500
600
700
800
900
1000
time (h)
'
T=200 K
~ 270 hours of aging
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Disorder in Regular Ferroelectrics. KDP family
36Physics 403 Spring 2020
Aging does not significantly change the domain
pattern of the KDP-DKDP ferroelectric. The
rearrangements in domain walls are responsible for
the decrease of the susceptibility.
t = 0 t = 10 h
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Disorder in Regular Ferroelectrics. KDP family
37Physics 403 Spring 2020
Finally, at low T these nanoscale polarized regions
becomes frozen and do not more contribute low
field susceptibility.
100 120 140 160 180 2000.0
0.2
0.4
0.6
0.8
100Hz
T (K)
'/1
00
0
155 160 165 170 175
20
40
60
80 100 Hz
500 Hz
1 kHz
2 KHz
5 KHz
10 kHz
20 kHz
T (K)
''
Tmax
165.0 165.5 166.0 166.5 167.04
6
8
10
ln(f
)
Tmax (K)
0
max
exp a
VF
Ef f
T T
−=
−
TVF=163.5 KPMN
DKDP
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Physics 403 Spring 2020 38
Applications of Ferroelectrics
KDP single crystals are mostly used as nonlinear optical materials
KDP powder is widely used as fertilizer
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0.0 0.1 0.2 0.3 0.4 0.5
300
400
500 Literature data
single crystals
ceramicsT
c (K
)
x
(PMN)(1-x)(PT)(x)
phase diagram
“Relaxor”
Ferroelectric
Paraelectric
(cubic)
(PMN)0.9(PT)0.1(PMN)0.7(PT)0.3
(PMN)0.6(PT)0.4
(PMN)0.97(PT)0.03
PT: PbTiO3, ferroelectric with
Curie temperature 763K
Solid solution relaxor-regular ferroelectric.
39Physics 403 Spring 2020
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Courtesy of D. Tenne, Boise State University40Physics 403 Spring 2020
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Courtesy of D. Tenne, Boise State University41Physics 403 Spring 2020
Applications of Ferroelectrics. Physics 403 Lab
AFM experimentQuantum Optics
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Applications. Nonvolatile Memory
Fast write speed (65-70ns)High endurance (1014 cycles)Low power consumption
42Physics 403 Spring 2020
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Applications. Actuators
Piezo-injector for diesel engines, (b) Multilayer piezoelectric actuator scheme.
(a)
(b)
Courtesy Technische Universität Darmstadt
Atomic Force Microscope
Lead Zirconium Titanate piezo scanner
PI (www.pi.ws)
43Physics 403 Spring 2020
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Applications. SonarsMilitary Applications
44
APPLICATIONS:
MINE HUNTINGWEAPONS SONARCOUTERMEASURESACOUSTIC COMMUNICATIONSPROJECTOR ARRAYSHYDROPHONE ARRAYSVIBRATION CONTROL
Piezocomposite materials have been testedby the United States military since 1992.
Physics 403 Spring 2020
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Applications. SonarsCivil Applications
45
Courtesy
Fish Finder
Physics 403 Spring 2020
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46
Applications. Adaptive Optics
Reflecting surface
Soldered control and mass wires
Courtesy of
http://scmero.ulb.ac.be
PZT – Lead Zirconium Titanate Pb[ZrxTi1-x]O3
Physics 403 Spring 2020
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47
Material Dielectric
constant
Piezoelectric
coefficient, (pC/n)
Electromechanical
coupling factorQuartz 4.5 2.3 0.1
Rochelle salt (30C) 9.2 27 0.3
Barium titanate
ceramic
1700 190 0.52
Lead zirconate
titanate PZT 45/55
450 140 060
PMN-PT (sc) 4200 2200 0.92-0.94
PZN-PT (sc) 2500 2400 0.91-0.93
Actuators TransducersAdaptive opticsCapacitorsLine motors for SFM
Transducer stack for
ultrasonic sonar application
(TRS Ceramics)
Piezoelectric
properties of different
materials
Ferroelectricity: Relaxors - aplications
Physics 403 Spring 2020