High resolution x ray diffraction study of phase and domain structures and thermally induced phase transformations in PZN (4 5 9)%PT 1

2.3 Paradigms of Relaxor Ferroelectric Single Crystals Thus Far 2.3.1 Bulk Phase Transformation and Domain Studies 2.3.2 Surface Layer and Dual Phases Chapter 3 Statement of Present Res

HIGH-RESOLUTION X-RAY STUDY OF PHASE AND

DOMAIN STRUCTURES AND THERMALLY-INDUCED

PHASE TRANSFORMATIONS IN PZN-(4.5-9)%PT

CHANG WEI SEA

NATIONAL UNIVERSITY OF SINGAPORE

2009

HIGH-RESOLUTION X-RAY STUDY OF PHASE AND

DOMAIN STRUCTURES AND THERMALLY-INDUCED

PHASE TRANSFORMATIONS IN PZN-(4.5-9)%PT

CHANG WEI SEA

(B.Sc.(Hons.), UTM; M.Sc., NUS)

A THESIS SUBMITTED

FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

DEPARTMENT OF MECHANICAL ENGINEERING

NATIONAL UNIVERSITY OF SINGAPORE

2009

i

Acknowledgements

I would like to express my heartfelt gratitude to my supervisor, Assoc Prof

Lim Leong Chew for his constant encouragement and invaluable advice and guidance

throughout this research work

My gratitude also goes to Prof Tu Chih-Shun and his research group for

being supportive, caring, and helpful in numerous ways during my visit to Fu Jen

Catholic University, Taipei I have also received a great deal of support and been

fortunate to work with Dr Yang Ping, Miao Hua, and Prof Herbert O Moser at

Singapore Synchrotron Light Source; Dr Ku Ching-Shun and Dr Lee Hsin-Yi at

National Synchrotron Radiation Research Center, Taiwan Dr Yang Ping deserves a

special mentioning for ensuring smooth operation in diffraction experiments Special

thanks to Prof Amar S Bhalla for his invaluable suggestion on the initial experiment

My thanks and appreciation to technical staffs in Materials Science Lab,

namely, Thomas Tan, Ng Hon Wei, Abdul Kalim, and Maung Aye Thein; technical

staffs in Mechanical Engineering Fabrication Support Centre, namely Lam Kim Song,

Low Boo Kwan, and T Rajah for their help in machining work My appreciation also

goes to Microfine staffs Dr Jin Jing, Dr K K Rajan, Paul Lim, Lenson Lim, and Joy

Chuah for providing a good support in this work

Thanks to my friends for being there through good times and the bad and for

ii

all the great memories we have shared over these years

Finally, I am especially indebted to my parents for their love and continuous

moral support Without them, this work would never have been completed

This work was supported by Ministry of Education (Singapore) and National

University of Singapore, via research grants nos R-265-000-221-112,

R-265-000-257-112, R-265-000-261-123/490 and R-265-000-257-731

2.3 Paradigms of Relaxor Ferroelectric Single Crystals Thus Far

2.3.1 Bulk Phase Transformation and Domain Studies 2.3.2 Surface Layer and Dual Phases

Chapter 3 Statement of Present Research

3.1 Objective of Present Work

iv

3.2 Scope of Present Work

3.3 Organization of Remaining Chapters

Chapter 4 Experimental Details

4.1 Sample Cut and Dimensions

4.2 Sample Preparation for Surface Layer Study

4.2.1 Mechanical Polishing 4.2.2 Fracturing Technique

4.3 Surface Layer Identification Methods

4.3.1 Normal X-ray Diffraction

4.3.2 High-resolution Synchrotron Radiation

4.3.3 Polarized Light Microscopy

4.4 Phase Transformation Studies

4.4.1 Polarization Characterization Methods

4.4.1.1 Dielectric Permittivity 4.4.1.2 Thermal Current Density 4.4.2 Structural Studies

4.4.2.1 High-resolution Synchrotron Radiation 4.4.2.2 Polarized Light Microscopy

Chapter 5 Surface Layer in Relaxor Ferroelectric PZN-PT Single

Crystals

5.1 Introduction

v

5.2 Polished Surface vs Fractured Surface at Room Temperature

5.2.1 Effect of Polished Surface on X-ray Diffraction Results

5.2.2 Effect of Polished Surface on Polarized Light Microscopy Results

5.3 Stability of the Polishing-induced Surface Layer

5.3.1 Thermal Stability

5.3.2 Electrical Resistance

5.4 Summary of Main Observations

Chapter 6 Tetragonal Micro/Nanotwins and Thermally-induced

Phase Transformations in Unpoled PZN-9%PT

6.1 Introduction

6.2 Theoretical Considerations of Diffractions from (002) planes of

Perovskite Crystals

6.2.1 Monoclinic Diffractions 6.2.2 Tetragonal Micro/Nanotwin Diffractions 6.2.3 Crystal Group Theory of Phase Transformation

6.3 Evidence of Tetragonal Micro/Nanotwins in PZN-9%PT at Room

Temperature 6.4 Thermally-induced Phase Transformations in Unpoled PZN-9%PT

6.4.1 Temperature Dependent Polarization Characteristics 6.4.2 Structural Studies

6.5 Summary of Main Observations

vi

Chapter 7 Rhombohedral Micro/Nanotwins and Thermally-induced

Phase Transformations in UnPoled PZN-4.5%PT

4.5%PT

7.4.1 Temperature Dependent Polarization Characteristics 7.4.2 Structural Studies

7.5 Summary of Main Observations

Chapter 8 Rhombohedral and Tetragonal Micro/Nanotwins Mixture

and Thermally-induced Phase Transformations in

Unpoled PZN-(6-8)%PT

8.1 Introduction

8.2 Room Temperature Phases of PZN-(7-8)%PT

8.3 Nature of Rhombohedral and Tetragonal Micro/Nanotwin Mixture

in PZN-(7-8)%PT at Room Temperature 8.4 Thermally-induced Phase Transformations in Unpoled PZN-8%PT

8.4.1 Temperature Dependent Polarization Characteristics 8.4.2 Structural Studies

vii

8.5 Thermally-induced Phase Transformations in Unpoled PZN-7%PT

8.5.1 Temperature Dependent Polarization Characteristics 8.5.2 Structural Studies

8.6 Summary of Main Observations

Chapter 9 Revised Phase Diagram for PZN-PT and Other

Observations

9.1 Revised Phase Diagram of PZN-PT System

9.2 Room Temperature Phase of PZN-PT Single Crystals of Different

viii

Summary

Extensive (002)pc reciprocal space mappings have been performed on

annealed (unpoled) relaxor ferroelectric PZN-(4.5-9)%PT single crystals by means of

high-resolution synchrotron x-ray diffraction (HR-XRD) To avoid undesired surface

effects produced by mechanical polishing, a fracturing technique has been devised to

expose the relatively stress free crystal bulk for the HR-XRD study

Evidence for rhombohedral and tetragonal micro/nanotwins could be detected

in the crystals For PZN-(4.5)%PT, the room temperature rhombohedral phase exhibits

an extremely broad diffraction in most instances, being the convoluted peak of

{100}-type and {110}-type rhombohedral micro/nanotwin diffractions, while

respective micro/nanotwin diffractions could be resolved in a number of samples The

increased growth and transformation stresses in PZN-(6-8)%PT promote the

coexistence of rhombohedral and tetragonal micro/nanotwins at room temperature in

these crystals The tetragonal phase in this case is metastable stabilized by the residual

stress in the crystal, which partly transforms to the stable rhombohedral phase when

the residual stress in the surface layer is relieved by fracturing This accounts for the

absence of (001)T diffraction in the exposed surface layer of the annealed crystals At room temperature, PZN-9%PT consists predominantly of {110}-type tetragonal

micro/nanotwins which behave in a coordinated manner upon heating The fine details

ix

of the rhombohedral and tetragonal micro/nanotwin domains in PZN-PT single crystals

are deduced from the RSM results described above

Based on the above finding and results of the heating experiments, a revised

phase diagram of the PZN-xPT system is constructed An expanded morphotropic

phase boundary region is evident in the revised phase diagram, which spans from 0.06

≤ x ≤ 0.09 at room temperature The ease of twinning via micro/nanotwin formation

and the existence of the broad (rhombohedral+tetragonal) two-phase field may explain

the high piezoelectric properties of relaxor-based piezoelectric single crystals of

compositions within the expanded morphotropic phase boundary region

x

List of Figures

Fig 2.1 The interrelationship of symmetry elements and the subgroup ferroelectric

Fig 2.2 Schematic of ferroelectric hysteresis loop showing the spontaneous

polarization (P i ), remnant polarization (P r ), and coercive field (E c)

Fig 2.3 (a) The cubic perovskite-type structure ABO3 (b) The off-centering

perovskite ABO3 with ferroelectric behavior

Fig 2.4 The direction of the spontaneous polarization of non-centric of (a)

tetragonal, (b) orthorhombic, and (c) rhombohedral

Fig 2.5 Difference between normal and relaxor ferroelectric at

ferroelectric-to-paraelectric transition: (a) a sharp transition and (b) a gradual, broad-diffuse and dispersive transition

Fig 2.6 The strain-E-field behavior of single crystals and ceramic ferroelectric

Fig 2.7 The first phase diagrams of (a) PZN-PT and (b) PMN-PT

Fig 2.8 Polarization rotation path in between the R-T phase transformation of high

piezoelectric relaxor-based ferroelectric single crystals

Fig 2.9 New phase diagrams of (a) PZN-PT and (b) PMN-PT

Fig 2.10 Schematic of T nanotwin superlattice (101) twin planes are indicated by

dashed lines A T unit cell is highlighted by gray shadow in respective twin

variants The primitive superlattice translation vector is L The volume

fractions of the first and second twin variants are ω and 1- ω, respectively The bilayer basis thickness is T

Fig 2.11 (a) High-resolution TEM image taken from a [001] PMN-0.35PT single

crystal; (b) power spectrum (fast Fourier transform) obtained from the image; and (c) High-resolution TEM image taken from a [001] PMN-0.35PT single crystal The presence pf different domain regions in

the images designated as A, B, and C; the insets show power spectra (FFT) obtained from (i) region A and (ii) region C

xi

Fig 2.12 (a) The inside and outer layer structures of PZN-PT single crystal system,

and (b) the revised PZN-PT phase diagram

Fig 4.1 (a) A schematic showing the two matching slots along the [100] direction of

the bulk single crystal (b) A picture of the matching slots viewed under a stereo microscope The dotted line in (b) indicates the fractured plane

Fig 4.2 (a) Fractured plane of bulk single crystal for HR-XRD diffraction (b) A

picture of the fractured plane viewed under a stereo microscope

Fig 4.3 The schematic of (a) beamline of high-resolution x-ray diffractometry in

SSLS and (b) differential movement of the rocking curve and detector to produce a RSM

Fig 4.4 A picture of the ZFH ε’ measurement

Fig 4.5 A picture of the ZFH J measurement

Fig 4.6 (a) Temperature and (b) E-field dependent HR-XRD measurements

Fig 4.7 (a) Temperature dependent measurement for PLM studies (b) The

interaction of plane-polarized light and the anisotropy crystal

Fig 4.8 The (001)-projection of the corresponding crystal polarization

Fig 5.1 (002) XRD profiles of PZN-4.5%PT single crystal taken from (a)

as-polished surface and (b) fractured surface

Fig 5.2 Same as Figure 5.1 but after the fractured surface of the PZN-4.5%PT

crystal sample was polished with SiC papers of different particle sizes The

inset gives the intensity of the lower 2θ peak as a function of particle size

of the polishing medium

Fig 5.3 (a) (002) RSMs taken from the fractured surface of PZN-4.5%PT showing

only the main R (002) peak (b) Same as (a) but taken from the as-polished surface, showing the lower 2θ peak in the ω = 0° plane arising from the spreading (or splitting) of the (002)R diffraction out of the ω = 0° plane but

toward lower 2θ values only The intensity contours are on log scale

xii

Fig 5.4 (a), (c) and (e) (002) XRD profiles taken from the as-polished surface of

PZN-7%PT, PZN-8%PT and PZN-9%PT, respectively (b), (d) and (f) same

as (a), (c) and (e) but taken from the fractured surface

Fig 5.5 (a), (c) and (e) (002) RSMs taken from the as-polished surface of

PZN-8%PT, PZN-9%PT and PZN-10.5%PT, respectively (b), (d) and (f) same as (a), (c) and (e) but taken from the fractured surface The intensity contours are on log scale

Fig 5.6 Same as Figure 5.4(b) but after the fractured surface of PZN-7%PT crystal

sample was polished with SiC papers of different particle sizes

Fig 5.7 Surface domain patterns of the (001)-cut PZN-4.5%PT crystal plate (a)

after polishing along the [010]pc direction and (b) after repolishing in the [110]pc direction Arrows indicate the direction of polishing Note the realignment from (a) to (b) (c) The domain patterns in the underlying material revealed by the focusing technique

Fig 5.8 No clear surface domain patterns of (001)-cut PZN-4.5%PT crystal plate as

a result of none crystallographic polishing direction

Fig 5.9 (002) XRD profiles of as-polished (solid curve) and differently annealed

(dashed curves) PZN-4.5%PT showing the effects of the different

annealing treatments on the lower 2θ peak Sample thickness is 1mm

Fig 5.10 (002) RSM taken from the as-polished surface of annealed PZN-4.5%PT,

showing the smeared contour lines over the area in the lower 2θ sides of

the main (002)R peak despite after annealing at 600 °C for 5 h The intensity contours are on log scale

Fig 5.11 (a), (c) and (e) (002) mappings taken from the as-polished surface of

PZN-7%PT, PZN-8%PT and PZN-9%PT after annealing at 257 °C for 1 h, respectively (b), (d) and (f) same as (a), (c) and (e) but taken from the fractured surface The intensity contours are on log scale

Fig 5.12 Effect of increasing poling field on the lower 2θ peak for as-polished

samples without any prior annealing Note that the lower 2θ peak is largely

eliminated after poling to 1.5 kV/mm Sample thickness is 1mm

xiii

Fig 5.13 Same as Figure 5.12 but for sample annealed at 600 °C for 1 h prior poling

treatment Note the persistence of the lower 2θ peak after poling to 1.5

kV/mm at room condition Sample thickness is 1mm

Fig 6.1 (a) M A , (b) M B , (c) M C , and (d) the relation between M C and O lattice

Fig 6.2 (002) diffraction intensity weighted distributions arising from (a) T

microdomains, (b) interference effect of T nanodomains and (c) combined effect of (a) and (b) (d) to (g) show the projections of various T

diffractions onto the (002) RSM; i.e., diffractions arising from (d) untilted

T microdomains; (e) tilted T microdomains; (f) streaking effect of untilted

T nanodomains, (i) streaking effects of tilted T nanodomains, and (l) combined diffraction patterns of T micro/nanodomains of all configuration

Fig 6.3 Lines between space groups indicate a group-subgroup relationship Solid

lines indicate a first-order transformation Dashed lines indicate a second-order transformation

Fig 6.4 Temperature dependent (002) RSMs taken at (a) 25 ºC, (b) 70 ºC, (c) 125

ºC, (d) 170 ºC, and (e) 180 ºC The {110}-type T twin planes are indicated

by white dashed line in (c) The intensity contours are on log scale

Fig 6.5 The diffraction planes are (a) parallel to the specimen with ω = 0º plane; (b)

inclined at angle ∆ω, and the corresponding RSMs for micro- and nanoscale domains

Fig 6.6 Schematic illustration of coexistence of both untilted and tilted (100)T and

(001)T micro/nanodomains in PZN-9%PT single crystal The tilted twins give rise to the off ∆ω = 0° diffractions with ∆ω/2 ≅ 0.22º for the (100)T

component and ∆ω/2 ≅ 0.61º for the (001)T component, respectively The

{110}-type T twin planes are indicated by red dashed lines

Fig 6.7 (a) ∆ω/2 and (b) Bragg’s position of (100)T and (001)T components of the

{110}-type T twins as a function of temperature The T-C phase

transformation occurs at 180 ºC

Fig 6.8 (a) ZFH ε’ and (b) ZFH J of unpoled (annealed) PZN-9%PT crystal The

sample thickness is 1.0 mm

xiv

Fig 6.9 Temperature dependent (002) RSMs taken from fractured surface of

annealed PZN-9%PT crystal obtained at (a) 25 ºC, (b) 55 ºC, (c) 70 ºC, (d)

100 ºC, (e) 125 ºC, (f) 140 ºC , (g) 160 ºC, (h) 170 ºC, and (i) 178 ºC The

intensity contours are on log scale The PZN-9%PT crystal consists of T

micro- and nanotwin domains and undergoes a sequence of

(R+T+T*)–(T+T*)–C phase transformation upon heating

Fig 6.10 ZFH domain structure of annealed PZN-9%PT crystal observed at by the

PLM (a) 25 ºC (P/A = 0º), (b) 25 ºC (P/A = 45º), (c) 55 ºC, (d) 65 ºC, (e)

125 ºC, (f) 145 ºC , (g) 170 ºC, and (h) 178 ºC The sample thickness is about 100 µm The dominant T domains coexist with the small fraction of

R domains at 25 °C The PLM observation is consistent with the HR-XRD results

Fig 7.1 (a) Schematic domain configuration of an unpoled R crystal structure with

spontaneous polarization directed along eight <111>pc direction (b) Three

dimensional illustration of a stereographic projection of the unpoled R

structure In the two dimensional plane, only the four <111>pc variants are projected

Fig 7.2 (a) Four of the eight <111>pc domain variants with tilt angle in both the ω

and 2θ planes (b) Each variant diffraction is represented by circles of half-intensity contours Individual variant diffractions broaden as a result

of residual stresses arising from the crystal growth process and accompanied phase transformations during cooling of the crystal to room conditions The resultant RSM pattern is given in (b)-(d) In the actual mapping, the detected diffractions are restricted to within the region of dotted lines in (b) (d) The projection of the convoluted peak(s) on (002) RSM

Fig 7.3 (a) The constructive interference effect of the two parent streaked of

{100}-type R nanotwin diffractions (b) The resultant nanotwin diffractions for {100}-type R nanotwins (c) The projection of such extra peak joining the two parent nanotwin diffractions on (002) RSM for the {100}-type R

nanotwins Traces of the twin type are laid along the <100>pc direction

Fig 7.4 (a) The constructive interference effect of the two parent streaked of

{110}-type R nanotwin diffractions (b) The resultant nanotwin diffractions for {110}-type R nanotwins (c) The projection of such extra peak joining

xv

the two parent nanotwin diffractions on (002) RSM for the {110}-type R

nanotwins Traces of the respective twin type are laid along the <110>pc

direction

Fig 7.5 (a) The projection of coexistence of the {100}-type and {110}-type R

nanotwins onto the (002) RSM (b) The projection of the coexistence of R

micro- and nanotwins onto (002) RSM

Fig 7.6 Room temperature HR-XRD (002) RSM of unpoled (annealed)

PZN-4.5%PT single crystals (a) shows a broad convoluted R peak while (b) shows evidence of R micro- and nanotwins These diffraction patterns indicate the possible coexistence of {100}-type and {110}-type R* (see

text for details)

Fig 7.7 (a) ZFH ε’ and (b) ZFH J of unpoled (annealed) PZN-4.5%PT crystal The

sample thickness is 1.0 mm A broad-diffuse and dispersive phase

transition in ε’ not only gives rise to a range of T max, but may mask the

weak anomalies in the ε’ curves

Fig 7.8 Temperature dependent (002) RSMs taken from fractured surface of

annealed PZN-4.5%PT crystal obtained at (a) 25 ºC, (b) 125 ºC, (c) 129 ºC, (d) 135 ºC, (e) 145 ºC, (f) 146 ºC, (g) 148 ºC, (h) 155 ºC, and (i) 160ºC The intensity contours are on log scale The PZN-4.5%PT undergoes a

transformation sequence of R*–(R*+T+T*)–T–(T+T*+C)–C upon heating

Fig 7.9 ZFH domain structures of annealed PZN-4.5%PT crystal observed by the

PLM at (a) 25 ºC, (b) 126 ºC, (c) 136 ºC, (d) 146 ºC, and (e) 154 ºC The sample thickness is about 50 µm The PLM observation is consistent with the HR-XRD results

Fig 8.1 Room temperature HR-XRD (002) RSMs of unpoled (annealed) (a) and (b)

PZN-7%PT, and (c) and (d) PZN-8%PT single crystals

Fig 8.2 Temperature dependent (002) RSMs taken from fractured surface of

annealed PZN-8%PT crystal obtained at (a) 25 ºC, (b) 80 ºC, and (c) 95 ºC The intensity contours are on log scale

Fig 8.3 Temperature dependent (002) RSMs taken from fractured surface of

another annealed PZN-8%PT crystal of predominantly R phase to begin

xvi

with at room temperature: (a) 25 ºC, and (b) 90 ºC The intensity contours are on log scale

Fig.8.4 Volume expansion associated with T-R transformation in PZN-PT single

crystals Note that the abrupt increase in volume associated with the

transformation when x > 0.07

Fig 8.5 Domain configurations of coexistence R* and T* domain structures The

arrows represent the directions of the polar axis in T phase The two polar directions are joined by the {110}-type T* as indicated by the red solid

lines The {110}R//{110}T interface are indicated the by blue solid lines

Note that the Tσ phase is metastable in this case, stabilized by the residual stress in the crystal

Fig 8.6 Geometry of the {110}R//{110}T interface (in blue) and domain

arrangement in the mixture of R and Tσ phases The {110}R//{110}T

interface is either (a) perpendicular to or (b) lying at 45° to the (001) diffracting plane

Fig 8.7 Schematic illustrations of the two-phase coexistence, R and T σ after

fracturing (a) For {110}R//{110}T interface perpendicular to the (001) diffracting plane, the effect of stress relaxation produced by fracture is not

as significant Thus, the Tσ phase remains metastable and both R and (100) T

can be detected from the fractured surface (b) For slant {110}R//{110}T

interface, the constraints produced by the neighbouring R phase in the crystal is removed by fracturing, causing the Tσ phase to transformed to the

R phase in the surface layer Thus, only R diffraction can be detected from

the fractured surface For x-ray of low energy as in the present work, the diffraction profile thus depends on the penetration depth in the (see text for details)

Fig 8.8 Room temperature HR-XRD (002) RSM of an as-grown (unpoled)

PZN-6%PT Peaks d3, d4 and d5 are R* diffractions, while peaks d1 and d2

are the (100)T diffraction and (001)T microtwin diffractions, respectively (see text for details)

Fig 8.9 (a) ZFH ε’ and (b) ZFH J of unpoled (annealed) PZN-8%PT crystal The

sample thickness is 1.5 mm

xvii

Fig 8.10 Temperature dependent (002) RSMs taken from fractured surface of

annealed PZN-8%PT crystal obtained at (a) 25 ºC, (b) 80 ºC, (c) 95 ºC, (d)

120 ºC, (e) 140 ºC, (f) 150 ºC , (g) 160 ºC, (h) 165 ºC, and (i) 173 ºC The intensity contours are on log scale The PZN-8%PT undergoes a

transformation of (R*+Tσ)–(R*+Tσ+T)–T–(T+T*+C) –C upon heating

Fig 8.11 ZFH domain structures of annealed PZN-8%PT crystal observed by the

PLM at (a) 25 ºC, (b) 85 ºC, (c) 105 ºC, (d) 145 ºC, (e) 165 ºC, and (f) 168

ºC The sample thickness is about 100 µm The PLM observation is consistent with the HR-XRD results

Fig 8.12 (a) ZFH ε’ and (b) ZFH J of unpoled (annealed) PZN-7%PT single crystal

The sample thickness is 1.0 mm

Fig 8.13 Temperature dependent (002) RSMs taken from fractured surface of

annealed PZN-7%PT crystal obtained at (a) 25 ºC, (b) 95 ºC, (c) 100 ºC, (d)

105 ºC, (e) 115 ºC , (f) 140 ºC, (g) 155 ºC, (h) 160 ºC, and (i) 168 ºC The intensity contours are on log scale The PZN-7%PT undergoes an

(R*+Tσ)–(R*+Tσ+T)–(T+T*)–(T+T*+C)–C phase transformation sequence

upon heating

Fig 8.14 ZFH domain structures of annealed PZN-7%PT crystal observed by the

PLM at (a) 25 ºC, (b) 100 ºC, (c) 110 ºC, (d) 125 ºC, (e) 145 ºC, and (f) 165

ºC The sample thickness is about 100 µm The PLM observation is thus consistent with the HR-XRD results

Fig 9.1 The revised phase diagram of PZN-PT system with extended (R+T) MPB

region The extended (R+T) MPB region can be divided into two regions

In the lower PT region, 6% ≤ x ≤ 8%, the T phase is metastable, denoted by

T σ. The Tσ is stabilized by the residual stresses in the crystal In the high PT

region, 9% ≤ x ≤ 10.5%, both the R and T are thermodynamically stable at room temperature A two-phase (T+C) coexistence region was detected at

high temperature before the crystal transforms to a single C phase

Fig 9.2 HR-XRD diffraction patterns of unpoled (a) PZN-4.5%PT, (b) PZN-7%PT,

and (c) PZN-8%PT at room temperature The a R and αR of the respected crystals are given in Table 9.1

Fig 9.3 Room temperature (002) RSMs of annealed-and-optimally-poled (a)

xviii

PZN-4.5%PT and (b) PZN-7%PT single crystals The poling field is normal

to the (001)pc diffraction plane The intensity contours are on log scale (c) and (d) show the RSMs of their unpoled counterparts for comparison purposes

Fig 9.4 E-field dependent (002) RSMs taken at (a) 0 kV/mm, (b) 0.5 kV/mm, and

(c) 0.8 kV/mm from the fractured surface of [001]-poled PZN-9%PT The

E -field dependent RSM reveals an (R+T)–T transformation under an

E-field application along [001]pc direction The intensity contours are on log scale

Fig 9.5 PP-ZFH J of the [001]-annealed-and-poled (a) PZN-4.5%PT and (b)

PZN-7%PT single crystals

Fig 9.6 PP-ZFH ε’ curves of the [001]-annealed-and-poled PZN-4.5%PT and

PZN-7%PT single crystals from which the “T R-T” was determined from the first anomaly

Fig 9.7 Temperature dependent (002) RSMs taken from fractured surfaces of the

[001]-annealed-and-poled PZN-4.5%PT single crystal: (a) 100 ºC, (b) 125

ºC, and (c) 135 ºC The intensity contours are in log scale T# indicates the

vague T diffractions T NT denotes the T at ∆ω ≠ 0º

Fig 9.8 Temperature dependent (002) RSMs taken from fractured surfaces of the

[001]-annealed-and-poled PZN-7%PT single crystal: (a) 105 ºC, (b) 110 ºC,

and (c) 115 ºC The intensity contours are in log scale T# indicates the

vague T diffractions T NT denotes the T at ∆ω ≠ 0º

Fig 9.9 Dielectric hysteresis behaviors of [001]-poled PZN-4.5%PT recorded

during the heating-cooling cycles to (a) 100 ºC, (b) 105 ºC, (c) 115 ºC, and (d) 125 ºC, respectively After heating to 105 ºC, PZN-4.5%PT showed clear signs of hysteresis on cooling to room temperature Above this temperature, the area of the dielectric hysteresis increases with increasing heating temperature The heating and cooling rate is 1.5 ºC/min

Fig 9.10 (a) K T and (b) k 31 of four plate samples of [001]-poled PZN-4.5%PT taken

at room temperature after cooling from the temperatures indicated on the

x-axis Both the K T and k 31 of PZN-4.5%PT started to degrade after it was

heated to 105 ºC

xix

List of Tables

Table 2.1 Work performed thus far on phases and domain studies of PZN-PT

Table 4.1 The optical and crystallographic properties pf the seven crystal systems

Table 4.2 Optical extinction angles of various phases along (001)-projection

Table 6.1 Relationship between the m and pc axes for various M phases and the O

phase in the unpoled state

Table 9.1 Deduced lattice parameters for the R phase at room conditions

Table 9.2 T DP , T R-T (L) and T R-T (U) of [001]-poled PZN-PT single crystals

HR-XRD : High-resolution synchrotron x-ray diffraction

RSM : Reciprocal space mapping

PLM : Polarized light microscope

xxi

FWHM : Full-width-at-half-maximum

ε’ : The real part of the dielectric permittivity

J : Thermal current density

dP/dt : Change in polarization per unit time

T max : Temperature at which the ε’ is at its maximum

T DP : The depolarization temperature which perceptible degradation of

dielectric and electromechanical properties begins

T R-T : The rhombohedral-to-tetragonal transformation temperature

T R-T (L) : Temperature at which rhombohedral-to-tetragonal transformation

begins

T R-T (U) : Temperature at which rhombohedral-to-tetragonal transformation

completes

xxii

k 31 : Electromechanical coupling constant

K T : Dielectric constant

MPB : Morphotropic phase boundary

SSLS : Singapore Synchrotron Light Source

TEM : Transmission electron microscope

1

Chapter 1

Introduction

Touted as next-generation materials for future high-performance transducers,

sensors, and actuators, relaxor-based ferroelectric single crystals of

Pb(Zn1/3Nb2/3)O3–PbTiO3 (PZN-PT) and Pb(Mg1/3Nb2/3)O3–PbTiO3 (PMN-PT)

solid-solutions display superior piezoelectric and electromechanical properties (i.e.,

with d33 > 2500 pC/N, k33 > 90%, maximum strain > 1.7%) [1] compared with

state-of-the-art Pb(Zr1-xTix)O3 (PZT or lead zirconate titanate) The astonishing

performance has driven intense research on physical properties of these materials to

aid the development of ferroelectric devices

Over the past decade, three theoretical considerations have been postulated in

explaining the superior properties of PZN-PT single crystals In the first, the superior

properties have been attributed to the result of polarization rotation, suggesting that the

presence of lower symmetry phases, i.e., monoclinic (M) phases act as the structural

bridge between the rhombohedral (R) and tetragonal (T) phase transformation In the

second, the superior properties are explained by the soft elastic constants of R structure

which inherently infers a large piezoelectric distortion, resulting in a strained or

distorted R phase (instead of the M phases) In the third, the adaptive ferroelectric

2

phase model and micro/nanotwin diffraction theories suggest that the observed M

diffractions may in fact be those of coherent diffractions of rhombohedral

micro/nanotwin (R*) and tetragonal micro/nanotwin (T*) domains

In addition to the paradigms described, contradictions associated with the

surface layer in relaxor ferroelectric have led to difficulties in structural analysis and

result interpretation

In this work, PZN-PT single crystals of (001)-orientation of different PT

contentswere prepared and studied Experimental analysis involving polarization and

structural characteristics has been performed on the unpoled (annealed) single crystals

as a function of temperature, in an attempt to understand the structural evolution of the

bulk single crystals upon heating Of particular focus in this work is the determination

of micro- and nanotwin domains in the bulk PZN-PT single crystals by means of

high-resolution diffraction study The phase diagram of PZN-PT system has been

amended based on the new results obtained in the present work

3

Chapter 2

Literature Survey

2.1 Background

Research in ferroelectric materials began to flourish when high dielectric

properties of barium titanate (BaTiO3) were reported independently by Wainer and

Salomon (United States), Ogawa (Japan), and Wul and Goldman (Russia) during

Second World War In the 1950s, relaxor ferroelectric PZT ceramic was discovered

The development of PZT based ceramics is among the most technologically important

events in which new piezoelectric devices notably transducers, sensors and actuators,

hydrophones, sonars, ultrasound medical imaging probes and many more have been

established To-date, PZT remains as the material of choice in most piezoelectric

devices However, the drawbacks of PZT, namely, fatigue, leakage current, and aging,

hamper their use in high performance devices [2-5] New materials of high dielectric

and electromechanical properties, either in the form of ceramics or single crystals, are

developed continuously and have extended to many mixed crystal systems since then,

including PZN-PT, PMN-PT, Pb(In1/2Nb1/2)O3–PbTiO3 (PIN-PT), and

Pb(Ni1/3Nb2/3)O3–PbTiO3 (PNN-PT)

4

2.1 Ferroelectrics

Crystals are classified into 32 crystal classes or point groups, which are

subdivided into seven basic crystal systems: triclinic, monoclinic, orthorhombic,

tetragonal, rhombohedral, hexagonal, and cubic Figure 2.1 shows the interrelationship

of the symmetry elements and the subgroup ferroelectrics Of the 32 crystal classes, 11

of them posses a centrosymmetry and the remaining 21 are non-centrosymmetry The

centrosymmetry crystals lead to no polar characters The non-centrosymmetry crystals

with the exception of point group 432, on the other hand, exhibit electric polarity when

subject to stress This effect is called piezoelectric effect Of the 20 piezoelectric

classes, 10 crystal classes are designated as pyroelectric due to the ability to possess

temperature dependent spontaneous polarization When the spontaneous polarization is

reversible by an applied E-field, the crystal is said to show ferroelectric behavior The

ferroelectric hysteresis loop and the important parameters are illustrated in Figure 2.2

2.2.1 Properties of ferroelectrics

2.2.1.1 Piezoelectric effect

Piezoelectricity defines the ability of certain crystals (the 20 piezoelectric

classes) to become electrically polarized when they are mechanically stressed, and vice

versa The first is known as direct piezoelectric effect and the latter is converse

5

Figure 2.1 The interrelationship of symmetry elements and the subgroup

ferroelectric

32 Symmetry Point Groups

21 Non-centrosymmetry

11 Centrosymmetry

20 Piezoelectric class

10 Pyroelectric

Subgroup Ferroelectric

- Spontaneously polarized

- Polarization reversible

6

Schematic of ferroelectric hysteresis loop

Figure 2.2 Schematic of ferroelectric hysteresis loop showing the

spontaneous polarization (Ps), remnant polarization (Pr), and

coercive field (Ec)

P

7

piezoelectric effect:

(direct piezoelectric effect) (2.1)

(converse piezoelectric effect) (2.2)

where P i is the induced polarization along the i direction in response to the applied stress σ jk with denoting the stress tensor elements and d ijk is the piezoelectric

coefficients For the converse effect, ε jk denotes as the strain tensor and E i denotes the

applied E-field within the crystal along the i direction The piezoelectricity is a linear

effect

The interaction between electrical and mechanical energies in piezoelectric

crystals implies a coupling between the two said forms of energy The

electromechanical coupling factor k is defined as:

energy)mechanical

or l(electricaenergy

ofInput

energy)mechanical

or l(electricaenergy

converted

The electro-optic effects describe the phenomenon that the optical properties

of a crystal can be altered through modification of refractive index by an E-field

Changes in refractive index lead to difference in birefringence Such effects are called

Kerr effect, and Pockels effect:

8

where n is the refractive index and E the applied electric field The coefficients a 1 and

a 2 are linear electro-optic and second-order electro-optic coefficient, respectively All materials exhibit Kerr effect, whereas only crystals that are non-centrosymmetric

exhibit Pockels effect

2.2.1.3 Perovskite-oxide Type

From Figure 2.1, it is recognized that in ferroelectric crystals, other than the

ferroelectric effect, they have also gathered both the piezoelectric and pyroelectric

effects, making them potential smart materials with unprecedented physical properties

and qualities Thus, they play an important role in piezoelectric, pyroelectric and

dielectric devices and continued to receive attention by contemporary scientists and

engineers

Of the four types of ferroelectrics: (1) the tungsten-bronze group, (2) the

oxygen-octahedral group, (3) the pyrochlore group, and (4) the bismuth layer-structure

group [6-7], the oxygen-octahedral group with perovskite-type structure ABO3 is by

far the most extensively investigated ferroelectric material Figure 2.3(a) shows the

perovskite structure ABO3, with A atoms situated at the cubic corners, B atoms the

effect)(Kerr

effect)(Pockels

9

body centers, and the oxygens at the face centers, where A is a monovalent, divalent or

tetravalent metal, and B a pentavalent, tetravalent or trivalent element, respectively

Often, at low temperatures, the perovskite structure is distorted in such a way that B or

O ions are tilted from the ideal positions with respect to A ions This off-centering

phenomenon leads to the presence of electric dipoles and thus the ferroelectric

behavior (Figure 2.3b) Figure 2.4 shows the different states of polarization direction in

various crystal structures Typically, at temperature well above Curie temperature (T C)

at which ferroelectric-to-paraelectric phase transition occurs, the perovskite structure is

in cubic phase which shows no ferroelectric behavior

Many relaxor-based ferroelectric known today are mostly lead-based

perovskite type compounds, having the general formula Pb(B’B”)O3 and

Pb(B’B”)O3-PbTiO3, where B’ is low valence cation, i.e., Zn, Mg, In or Ni, and B” is

high valence cation, i.e., Nb, Ta or W [8] These compounds differ from classical

perovskite, i.e., the normal type ferroelectric BaTiO3 and PbTiO3 (PT or lead titanate)

with the general formula ABO3 The presence of heterovalent B-site ions in relaxor

ferroelectric are randomly distributed on the cation sites Due to statistical distribution,

the randomly different cation charges give rise to random fields which tend to make

the ferroelectric-to-paraelectric transition diffuse and dispersive instead of a sharp

transition as in the normal type ferroelectric [7] Figure 2.5 shows the difference in

10

Figure 2.3 (a) The cubic perovskite-type structure ABO3 (b) The

off-centering perovskite ABO3 with ferroelectric behavior

11

Figure 2.4 The direction of the spontaneous polarization of non-centric of

(a) tetragonal, (b) orthorhombic, and (c) rhombohedral [9].

12

ferroelectric-to-paraelectric transition behavior between the normal and relaxor

ferroelectrics The relaxor ferroelectric displays a broad-diffuse and dispersive phase

transition leading to a range of dielectric maximum temperature, while the normal

ferroelectric shows a sharp transition The temperature dependence of the dielectric

constant above the ferroelectric-to-paraelectric transition can be described by the

Curie-Wiess law:

where ε m and T m are the dielectric maximum and the corresponding temperature When

γ = 1, the dielectric constant follows a normal Curie-Wiess type, showing a sharp

transition When γ = 2, the transition is a diffused-type

Today’s best known relaxor-based ferroelectrics PZN-PT and PMN-PT solid-

solution single crystals have been investigated extensively over the last decade

Interest in these materials has been driven by their excellent piezoelectric and

ferroelectric properties (i.e., piezoelectric coefficients, d33 > 2500 pC/N, strain > 1.7%,

electromechanical coupling, k33 > 90%) [1], making them candidate materials for high

performance device applications (Figure 2.6) Despite the extensive experimental and

theoretical studies, structural characteristic of the relaxor-based ferroelectrics remains

not fully understood

13

(a) Normal ferroelectric: PbTiO3

(b) Relaxor ferroelectric: PbMg1/3Nb2/3O3

Figure 2.5 Difference between normal and relaxor ferroelectrics at

ferroelectric-to-paraelectric transition temperature: (a) a sharp transition in normal ferroelectric, and (b) a gradual, broad-diffuse and dispersive transition behavior in relaxor ferroelectric

14

Figure 2.6 The strain-E-field behavior of single crystals and ceramic

ferroelectric [1]