1. Lead Magnesium Niobate (PMN) System

2. Lead Magnesium Niobate (PMN) System
Important Perovskite End Members for Relaxors
Important Relaxors Based on MPB Compositions

3. Lead Magnesium Niobate (PMN) System
Relaxor-Based Compositions for MLC

4. Lead Magnesium Niobate (PMN) System
Areas of Applications for Relaxors Ferroelectrics and Solid Solutions
Application
Example
Pyroelectrics
Capacitors/dielectrics
Electrostriction/actuators
Medical ultrasound/high
efficiency transducers
Piezoelectrics
Electrooptics
Pb(Sc1/2 Ta1/2)O3
(Ba0.60 Sr0.40)TiO3
Pb(Mg1/3Nb2/3)O3
Pb(Zn1/3Nb2/3)O3
Pb[(Mg1/3Nb2/3)1-xTix]O3
Pb[(Zn1/3Nb2/3)1-xTix]O3
Pb[(Sc½Nb½)1-xTix]O3
Pb(Zr1-xTix)O3
(Pb1-xLa2x/3)(Zr1-yTiy)O3

5. Lead Magnesium Niobate (PMN) System
Relaxor Ferroelectrics 
Pb(B1B2)O3
(B1 ~ lower valency cation : Mg2+, Zn2+, Ni2+, Fe3+)
(B2 ~ higher valency cation : Nb5+, Ta5+, W6+)
PMN  Pb(Mg1/3Nb2/3)O3
Important Relaxor Ferroelectric with Tc ~ -10 C
Broad diffused and dispersive phase transition on cooling below Tc
Very high room temperature dielectric constant
Strong frequency-dependent dielectric properties 
Nano-scaled compositional inhomogeniety
Chemically order-disorder behavior observed by TEM study
B-site 1:2 order formula with 1:1 order arrangement in the structure
(Most have rhombohedral symmetry due to slight lattice distortion)

6. Lead Magnesium Niobate (PMN) System
Dielectric properties of Pb(Mg1/3Nb2/3)O3
showing diffused phase transition and relaxor characteristics
(Tmax ( at 1 kHz) ~ -10 C with er max ~ 20,000)

7. Lead Magnesium Niobate (PMN) System
Property
Normal Ferroelectrics
Relaxor Ferroelectrics
Permittivity temperature dependence
Permittivity frequency dependence
Permittivity behavior in Paraelectric range
Remnant polarization (Pr)
Scattering of light
X-Ray diffraction
Sharp 1st or 2nd order transition about Tc
Weak frequency dependence
Follow Curie-Weiss Relation above Tc
Strong remnant polarization
Strong anisotropy (birefringent)
Line splitting (cubic to tetragonal)
Broad-diffused phase transition about Tmax
Strong frequency dependence
Follow Curie-Weiss Square Relation above Tmax
Weak remnant polarization
Very weak anisotropy to light (pseudo-cubic)
No line splitting (pseudo-cubic structure)
Comparison of normal and relaxor ferroelectrics

8. Lead Magnesium Niobate (PMN) System Spontaneous polarization (Ps)
First-Order Phase Transition
Second-Order Phase Transition
Spontaneous polarization (Ps)
A discontinuity in the first-order phase transition 
 A continuous change in the second-order phase transition 
Relaxor ferroelectric  Ps decays continuously with temperature,
but does not follow the parabolic temperature dependence
as in the second-order phase transition

9. Lead Magnesium Niobate (PMN) System
Normal Ferroelectrics
 Dielectric Behavior 
Relaxor Ferroelectrics
Normal ferroelectrics  the onset of spontaneous polarization occurs simultaneously with the maximum in the paraelectric to ferroelectric phase transition. No Ps above the transition temperature with a valid Curie-Weiss Law
Relaxor ferroelectrics  Three regimes : Regime I Above dielectric maximum temperature, Regime II Between Td (depolarization temperature) and Tmax (dielectric transition temperature), and Regime III Below Td

10. Lead Magnesium Niobate (PMN) System
Regime I : Electrostrictive region with existence of chemically ordered region with no macro-scale ferroelectric domian  little or no hysteresis
Regime II : Freezing-out of macro-domain region in which with decreasing temperature the polar regions grow and cluster  hysteresis is observed and becomes more pronounced with decreasing temperature
Regime III : Macro-domain region becomes more stable which results to a large spontaneous polarization and piezoelectric effects with large remnant strain

11. Lead Magnesium Niobate (PMN) System
Ordered and Disordered Perovskite Structures

12. Lead Magnesium Niobate (PMN) System
Ordered and Disordered Perovskite Structures
Fully disorder of the cations in the B-sites occupation 
“Normal” ferroelectric materials (such as PZT)
Nano-scale order of the cations in the B-sites occupation
“Relaxor” ferroelectric materials (such as PMN)

13. Lead Magnesium Niobate (PMN) System Diffused/broad dielectric behavior
5 nm
Nano-scale ordered region in disordered matrix
Pb(Mg1/3Nb2/3)O3 
Nano-scale ordered region with Mg:Nb = 1:1 (like in NaCl structure)
Non-stoichiometric short range chemical heterogeneity
Different ferroelectric transition temperature regions
Diffused/broad dielectric behavior

14. Lead Magnesium Niobate (PMN) System
PbSc1/2Ta1/2O3
Harmer and Bhalla
PbMg1/3Nb2/3O3
Randall et al.
Dark field TEM images showing nano-scale ordered region in disordered matrix

15. Lead Magnesium Niobate (PMN) System
Polarization
Dielectric
Hysteresis
Birefringence
Features for Ordered and Disordered Ferroelectrics

16. Lead Magnesium Niobate (PMN) System
Structural Transition
Ferroelectric properties decay with increasing T 
Features for Ordered and Disordered Ferroelectrics

17. Lead Magnesium Niobate (PMN) System
Relaxor Ferroelectrics 
PMN  Pb(Mg1/3Nb2/3)O3
Strong frequency-dependent dielectric properties
(Tmax shifts to higher temperature with increasing frequency)
(Dielectric losses are at the highest just below Tmax) 
Dynamical thermal re-orientation of polar regions with frequency
(As frequency increases, the polar regions cannot keep up  er  and loss )
Dielectric relaxation similar to glass (follows a Vogel-Fulcher model)
However, no certain explanation for relaxor ferroelectrics
Freezing of micro-region and chemical fluctuation 
 Ordered-disordered region 
 Spin-glass model 

18. Lead Magnesium Niobate (PMN) System
One of the difficulties in processing PMN ceramics 
Pyrochlore
(General formula RNb2O6 where R is a mixture of divalent ions)
Pb1.83Nb1.71Mg0.29O6.39  formed at C
Paraelectric with room temperature er of 130
Strong reduction in er if present as inter-granular region in high er PMN region
(Not very significant if only discrete particles disperse in PMN matrix)
Pure Phase PMN with “Columbite Precursor Method”
(MgO + Nb2O5  MgNb2O6  MgNb2O6 + PbO  PMN)
Example of Pyrochlore Phase

19. Lead Magnesium Niobate-Lead Titanate (PMN-PT) System
Most widely studied relaxor materials  PMN-PT Solid Solutions 
High-strain (0.1%) electrostrictive actuators
High dielectric constant (er > 25,000) capacitors

20. Lead Magnesium Niobate-Lead Titanate (PMN-PT) System
0.65 PMN PT  MPB Compositions with normal ferroelectric properties
High dielectric constant capacitors  0.90 PMN PT  Relaxor
(with Tmax near room temperature with large dielectric constant)
(large “electrostrictive” strain)

21. Lead Magnesium Niobate-Lead Titanate (PMN-PT) System
Dielectric Behavior of 0.9PMN-0.1PT Relaxor Ferroelectrics

22. Lead Magnesium Niobate-Lead Titanate (PMN-PT) System
Strain-Field Relation of 0.9PMN-0.1PT Relaxor Ferroelectrics

23. Lead Magnesium Niobate-Lead Titanate (PMN-PT) System
Electrostriction in Ferroelectric Materials 
Basis of electromechanical coupling in all insulators
x = ME2 and x = QP2
(As compared to x ~ E for piezoelectric effects)
Large in ferroelectrics just above Tc
due to electrical unstabability of ferroelectrics (PMN, PZN, and PLZT)
(because of their diffused transition and possible field-activated coalescence of micropolar region to macrodomain of the parent ferroelectric ) 
“Electrostrictive Mode”
“Field-Biased Piezoelectric Mode”
DC Bias Field  Induced Ferroelectric Polarization  Normal Piezoelectric
d33 = 2Q11P3e33
d31 = 2Q12P3e33

24. Lead Magnesium Niobate-Lead Titanate (PMN-PT) System
Advantages of Electrostriction 
Minimal or negligible strain-field dependence hysteresis
(in selected temperature range)
More stale realizable deformation than observed in piezo-ceramics
No poling is required
Longitudinal strain
0.1% in PMN
0.3% in PLZT (La/Zr/Ti = 9/65/35)
Disadvantages of Electrostriction
Limited usable temperature range 
(due to a strong temperature dependence)
 Small deformation at low electric field 
(as a result of a quadratic nature of electrostriction)

25. PMN-PT and PZN-PT Single Crystals
1-x PMN – x PT Single Crystals
x = 35 for MPB compositions
 Large piezoelectric strain > 1%
 High electromechanical coupling factor (k33 > 90%)
 Relaxor-based piezoelectric crystals for next generation transducers
1-x PZN – x PT Single Crystals
x = 9 for MPB compositions
 Large piezoelectric strain ~ 1.7%
 High electromechanical coupling factor (k33 = 92%)
 Relaxor-based piezoelectric crystals for high performance atuators

26. PMN-PT and PZN-PT Single Crystals
Comparison of field-induced strain for various ceramics and single crystals

27. PMN-PT and PZN-PT Single Crystals

28. PMN-PT and PZN-PT Single Crystals Engineered Domain States
Initially the domains are aligned as close as possible to the field direction
Increased polarization in rhombohedral structure
As the field is increased to certain values, the domains collapse to the <001> direction, as a result of rhombohedral-to-tetragonal phase transition
Large increase in polarization, hence piezoelectric properties