SYNTHESIS AND PHASE DIAGRAMS OF THE LEAD MAGNESIUM...
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SYNTHESIS AND PHASE DIAGRAMS OF THE LEAD MAGNESIUM NIOBATE - LEAD TITANATE - LEAD OXIDE SYSTEM Jingping (Jean) Gao B.Sc. Tianjin University, P. R. China, 1983 M. Sc. Beijing Vacuum Research Institute, P. R. China, 1990 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE In the Department of Chemistry O Jingping (Jean) Gao SIMON FRASER UNIVERSITY December 2003 All rights reserved. This work may not be reproduced in whole or in part, by photocopy or other means, without permission of the author.
Transcript of SYNTHESIS AND PHASE DIAGRAMS OF THE LEAD MAGNESIUM...
SYNTHESIS AND PHASE DIAGRAMS OF THE LEAD MAGNESIUM NIOBATE - LEAD TITANATE -
LEAD OXIDE SYSTEM
Jingping (Jean) Gao
B.Sc. Tianjin University, P. R. China, 1983 M. Sc. Beijing Vacuum Research Institute, P. R. China, 1990
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
In the Department
of Chemistry
O Jingping (Jean) Gao
SIMON FRASER UNIVERSITY
December 2003
All rights reserved. This work may not be reproduced in whole or in part, by photocopy
or other means, without permission of the author.
APPROVAL
Name: Jing-ping Gao
Degree: M.Sc.
Title of Thesis: Synthesis and Phase Diagrams of the Pb (Mg1,3Nb2/3)03- PbTi03-PbO System.
Examining Committee:
Chair: Dr. N.R. Branda, Associate Professor
Date Approved:
Dr. Z-G. Ye, Professor, Senior Supervisor
D r . R.H. Hill, Professor, Committee Member
--- Dr. G.W. ~eac$,!~ssociate ~rofessor,-committee Member
Dr. H.Z. Yu, Assistant Professor, Internal Examiner
PARTIAL COPYRIGHT LICENCE
I hereby grant to Simon Fraser University the right to lend my thesis,
project or extended essay (the title of which is shown below) to users of the
Simon Fraser University Library, and to make partial or single copies only
for such users or in response to a request from the library of any other
university, or other educational institution, on its own behalf or for one of its
users. I further agree that permission for multiple copying of this work for
scholarly purposes may be granted by me or the Dean of Graduate
Studies. It is understood that copying or publication of this work for
financial gain shall not be allowed without my written permission.
Title of Thesis/Project/Extended Essay:
Synthesis and Phase Diagrams of the Pb (Mg113Nb213)03-PbTi03- PbO System.
Author: - - . . . '(.si&ture)
Jing-ping Gao (name)
Dee 2 , Z c v 3 (date)
ABSTRACT
This work studied the high piezoelectric and ferroelectric solid solution of
(l-~)Pb(Mg~/~Nb~/3)0~-xPbTiO~ system [abbreviated as (I-x)PMN-xPT], including the
materials synthesis, phase stabilities by means of thermogravimetry/differential thermal
analysis (TGIDTA), phase structure and symmetry by the conventional x-ray diffraction
(XRD) and the high-resolution synchrotron x-ray diffraction.
Based on the high-resolution synchrotron x-ray diffraction analysis, a new phase
diagram of the (1-x)PMN-xPT system around the morphotropic phase boundary (MPB)
has been established. A monoclinic phase in the compositional range of 0.31 5 x 5 0.37
has been found. Lattice parameters are also calculated based on the synchrotron x-ray
diffraction data analyses. This low temperature phase diagram will help us to properly
understand the fine phase structure as well as the origin of the piezoelectric properties
around the morphotropic phase boundary.
Based on the differential thermal analysis data, a high temperature phase diagram
of (I-x)PMN-xPT solid solutions has been determined. This phase diagram has a solid
solution form with thermal minimum (T,, = 1280 "C) at 70 mol% PbTi03. The melting
point of PbTi03 measured from this experiment is 1286 "C. This high temperature phase
diagram provides the melting point data of the system and the information on the control
of the phase segregation between Pb(Mg1/3Nb2/3)03 (PMN) and PbTi03 (PT) during the
crystal growth.
A high temperature phase diagram of the pseudo-binary
(100-y)Pb(Mg1~3Nb~~3)~.65Tio,3503 - yPbO system [abbreviated as (100-y)PMNT65/35-
yPbO, y in wt%] has also been established based on the differential thermal analysis
measurements. The phase diagram shows that (100-y)wt%PMNT65/35-ywt%PbO system
has a eutectic melting behaviour with the eutectic composition of 20wt%PMNT65/35-
80wt%PbO. The eutectic temperature was determined at 846 +- 7 "C. This high
temperature phase diagram provides the melting and solidifying of the system, which is
useful for determining the temperature and the optimum flux (PbO) concentration for the
PMNT65135 crystal growth.
DEDICATION
This thesis is dedicated to
my beloved parents, Bowen Gao and Fengru Cheng,
my fully supporting husband, Hong Cao,
and my two lovely daughters, Diou and Laura.
ACKNOWLEDGEMENTS
I would like to express my sincere gratitude to my senior supervisor, Dr. Z.-G.
Ye, for giving me the opportunity to work in his laboratory, and for all his guidance,
support and encouragement throughout the course of this project.
I would like to thank the members of my supervisory committee, Dr. R. H. Hill
and Dr. G. W. Leach, for their valuable suggestions and advice.
I would like to thank Dr. H.Z. Yu for being the internal examiner of my thesis and
for his useful suggestions.
I am most grateful to Dr. B. Noheda, Dr. G. Shirane and Dr. D. E. Cox of
Brookhaven National Laboratory for collaborating in synchrotron XRD studies,
especially Dr. B. Noheda who performed the synchrotron XRD measurements and helped
analyzing the structures.
I would like to thank all members of Dr. Ye's research group, both past and
present, for their constant support and friendship, especially Dr. M. Dong, Dr. A. A.
Bokov and Ms. Y.-H. Bing.
Finally, my thanks go to the members of Chemistry Department at Simon Fraser
University for their support.
TABLE OF CONTENTS
. . APPROVAL ....................................................................................................................... 11
... ABSTRACT ..................................................................................................................... 111
DEDICATION ................................................................................................................... v
ACKNOWLEDGEMENTS ............................................................................................. vi
TABLE OF CONTENTS ................................................................................................ vii
LIST OF TABLES .......................................................................................................... ix
LIST OF FIGURES .......................................................................................................... x .. .......................................................... LIST OF ABBREVIATIONS AND SYMBOLS xu
Chapter 1 General Introduction ..................................................................................... 1 .............................................................................................. 1.1 Ferroelectric Materials 1
................................................................... 1.2 Development of Ferroelectric Materials 4 .................................. 1.3 (l-~)Pb(Mg~/~Nb~~)O~-xPbTi0~ (PMN-PT) Solid Solutions 7
1.4 Objectives of This Work .......................................................................................... 9 .............................................................................................................. 1.5 References 11
Chapter 2 Low Temperature Phase Diagram of (1-x)PMN-xPT Solid Solutions around the Morphotropic Phase Boundary ................................................. 14
2.1 Introduction ............................................................................................................ 14 2.1.1 The Structure of Relaxor Ferroelectrics around the Morphotropic Phase
Boundary .................................................................................................... 14 ........................................................................ 2.1.2 Synchrotron X-ray Diffraction 17
2.2 Experimental .......................................................................................................... 20 2.2.1 Preparation of Solid Solutions .......................................................................... 20
...................................................................... 2.2.2 Preparation of Ceramic Samples 23 ............................................... 2.2.3 Conventional X-ray Diffraction Measurements 23
2.2.4 Synchrotron X-ray Diffraction Measurements ................................................. 24 ........................................................................................... 2.3 Results and Discussion 25
....................................................................... 2.3.1 Conventional X-ray Diffraction 25 ......................................................................... 2.3.2 Synchrotron X-ray Diffraction 27
2.3.2.1 Analytical Steps of Synchrotron X-ray Diffraction Patterns .................... 27 ......... 2.3.2.2 Composition Effect on the Synchrotron X-ray Diffraction Patterns 27
2.3.2.3 Temperature Effect on the Crystal Structures ........................................... 32 2.3.2.4 Summary of the Composition Effect on the Lattice Parameters ............... 42
..................... 2.4 Phase Diagram in the Region of the Morphotropic Phase Boundary 45 2.5 Conclusions ........................................................................................................... 4 5
vii
2.6 References .............................................................................................................. 46
Chapter 3 High Temperature Phase Diagram of the (1-x)PMN-xPT Solid ........................................................................................................................... Solutions 48
............................................................................................................ 3.1 Introduction 48 ................................................. 3.1.1 Differential Thermal Analysis Measurements 50
3.1.2 Constructing a Phase Diagram from Differential Thermal Analysis Curves ............................................................................................................ 54
.......................................................................................................... 3.2 Experimental 56 .................................... 3.2.1 Sample Preparation for Differential Thermal Analysis 56
.................. 3.2.2 Thermogravimetry/Differential Thermal Analysis Measurements 57 ........................................................................................... 3.3 Results and Discussion 58
................................................................................. 3.3.1 X-ray Diffraction Spectra 58 .......................................... 3.3.2 TherrnogravimetrylDifferential Thermal Analysis 59
3.3.2.1 Effect of HeatingICooling Rate ................................................................. 61 3.3.2.2 Differential Thermal Analysis Results of (1-x)PMN-xPT Solid
Solutions .............................................................................................. 65 3.3.2.3 Determination of the Melting Point of PbTi03 ......................................... 67 3.3.2.4 (1-x)PMN-xPT Solid Solution Phase Diagram ......................................... 70
............................................................................................................ 3.4 Conclusions 73 .............................................................................................................. 3.5 References 73
Chapter 4 High Temperature Phase Diagram of [0.65Pb(Mg113Nb2,3)03- ............................................................................................... 0.35PbTi03].Pb0 System 76
4.1 Introduction ............................................................................................................ 76 ..................................... 4.1.1 Characteristic Temperatures of an Endothermic Peak 78
4.1.2 Constructing Eutectic Phase Diagram from Differential Thermal Analysis ....................................................................................................... 79
4.2 Experimental .......................................................................................................... 81 ........................................................................................... 4.3 Results and Discussion 82
................................................................................. 4.3.1 X-ray Diffraction Spectra 82 .......................................................................... 4.3.2 Differential Thermal Analysis 83
......................................... 4.3.2.1 Differential Thermal Analysis of PMNT65135 84 4.3.2.2 Differential Thermal Analysis of 60wt%PMNT65/35-40wt%PbO .......... 88 4.3.2.3 Differential Thermal Analysis of 90wt%PMNT65/35- 10wt%PbO .......... 90 4.3.2.4 Differential Thermal Analysis of lOwt%PMNT65/35-90wt%PbO .......... 92
................................ 4.3.3 Discussion on the Differential Thermal Analysis Results 93 ......................................... 4.3.4 PMNT65135 - PbO Pseudo-Binary Phase Diagram 96
............................................................................................................ 4.4 Conclusions 98 4.5 References ............................................................................................................. 9 8
..................................................................................................... Chapter 5 Summary 100
............................................................................... Appendix Pseudo-Voigt Function 102
viii
LIST OF TABLES
Table 1.1 Definitions of some physical quantities measuring the related ................................................................................... ferroelectric properties 3
Table 1.2 Development of some ferroelectric materials ......................................... 5
Table 1.3 Summary of the analytical tools and their intended functions ..................... 11
Table 2.1 Phase symmetry of some ferroelectrics around the morphotropic phase boundary .................................................................................................. 16
Table 2.2 Summary of phase symmetries and lattice parameters at 300 K for (1-x)PMN-xPT around the morphotropic phase boundary .............................. 31
Table 2.3 Summary of phase symmetries and lattice parameters at 20 K for (1-x)PMN-xPT around the morphotropic phase boundary .............................. 41
Table 3.1 Some melting points of (1-x)PMN-xPT solid solutions ........................... 49
Table 3.2 Effect of heatinglcooling rate on the meltinglsolidifying temperatures of 0.10PMN.0.90PT .......................................................................... 63
Table 3.3 Summary of the melting points of the (1-x)PMN-xPT solid solutions ............ 70
Table 4.1 Effect of heatinglcooling rates on the meltinglsolidifying temperatures for PMNT65135 .............................................................................. 86
Table 4.2 Summary of the peak temperatures upon heating for (100-y)wt%PMNT65/35-ywt%PbO system ............................................ 93
Table 4.3 Summary of the eutectic peak area obtained from differential thermal analysis for the PMNT65135-Pb0 system .............................................. 95
LIST OF FIGURES
Figure 1.1 Perovskite structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . ... ,. . ... . . .... 2
Figure 1.2 Development of the piezoelectric coefficient d33 for fernelectric materials ............................................................................................................... 6
Figure 2.1 Original low temperature phase diagram of the (1-x)PMN-xPT solid solutions.. . . . . ..... . . . .. . .. . .. . ... . .. .. . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . , . , , . . . . . . . . . . . . . . . . . . . . 15
Figure 2.2 Synchrotron radiation .................................................................................... 19
Figure 2.3 The cubic (1 11) reflection obtained from conventional x-ray diffraction and synchrotron x-ray diffraction ....................................................................... 20
Figure 2.4 Thermogravimetry/differential thermal analysis for the commercial MgO ................................................................................................................ 22
Figure 2.5 A segment of conventional x-ray diffraction spectrum for a PMN-39PT ceramic sample ..................................................................................................... 26
Figure 2.6 Synchrotron x-ray diffraction patterns of selected regions at 300 K with 0.70040 A for a) PMN-30PT, b) PMN-3IPT, c) PMN-33PT and d) PMN-39PT . . . ............................................................................................... 28
Figure 2.7 Synchrotron x-ray diffraction patterns of PMN-35PT at 450 K, 400 K and 20 K in the selected regions ........................................................................... 33
Figure 2.8 Variation of the lattice parameters as a function of temperature for PMN-39PT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . 35
Figure 2.9 Variation of the lattice parameters of the monoclinic phase as a function of temperature for PMN-3 1PT ... . . .. ... . ... . . . . .. . . .... .. .. . ... ... . . . . . . . . . . . . . . 37
Figure 2.10 Variation of the lattice parameters of the monoclinic phase as a function of temperature for PMN-33PT .............................................................. 38
Figure 2.11 Variation of the lattice parameters of the monoclinic and tetragonal phases as a function of temperature for PMN-37PT ............................................ 40
Figure 2.12 Variation of the lattice parameters of the majority phases as a function of PbTi03 concentration at 300 K ....................................................................... 43
Figure 2.13 Variation of the lattice parameters of the majority phases as a function of PbTi03 concentration at 20 K ........................................................................... 44
Figure 2.14 New phase diagram of (I-x)PMN-xPT solid solutions in the vicinity of the morphotropic phase boundary deduced from synchrotron x-ray diffraction results ..................................................................................... ............ 46
Figure 3.1 Schematic set-up of differential thermal analysis ......................................... 50
Figure 3.2 Typical endothermic and exothermic peaks of differential thermal ................................................................................................................. analysis 51
Figure 3.3 A typical endotherm showing the characteristic temperatures ...................... 53
Figure 3.4 A continuous solid solution phase diagram with superimposed ...................................................................... differential thermal analysis curves 55
.......................................................... Figure 3.5 Schematic sealing process for Pt tubes 57
Figure 3.6 Selected x-ray diffraction spectra of (1-x)PMN-xPT solid solutions ............ 58
Figure 3.7 Thermogravimetry profile of 0.40PMN-0.60PT sample ............................... 60
Figure 3.8 Effect of heatinglcooling rates on the meltinglsolidifying temperatures for O.lOPMN.0.90PT ........................................................................................... 62
Figure 3.9 Differential thermal analysis curves of 0.70PMN-0.30PT ............................ 66
........................................... Figure 3.10 Differential thermal analysis curves of PbTi03 69
Figure 3.1 1 High temperature phase diagram of the (I-x)PMN-xPT solid solutions .............................................................................................................................. 71
..................................... Figure 4.1 Characteristic temperatures of an endothermic peak 79
Figure 4.2 A eutectic phase diagram with superimposed differential thermal analysis curves ...................................................................................................... 80
Figure 4.3 X-ray diffraction pattern of 0.65PMN.0.35PT (PMNT65135) powder .......... 83
Figure 4.4 Differential thermal analysis curves of 0.65PMN-0.35PT (PMNT65135) at heatinglcooling rates of (a) 5 "Urnin and (b) 10 "Clmin ....... 85
Figure 4.5 Differential thermal analysis curves of 60wt%PMNT65/35-40wt%PbO
Figure 4.6 Differential thermal analysis curves of 90wt%PMNT65/35-10wt%PbO ....... 91
Figure 4.7 Differential thermal analysis curve of 10wt%PMNT65/35-90wt%Pb0 ....... 92
Figure 4.8 Determination of the eutectic composition from differential thermal analysis for the (100-y)PMNT65/35-yPbO system ............................................. 96
Figure 4.9 Phase diagram of the (1-y)PMNT65/35-yPb0 system .................................. 97
DTA
d33
f K33
k33
M
MPB
PMN
PMNT65135
PT
PZN
PZT
R
LIST OF ABBREVIATIONS AND SYMBOLS
Differential thermal analysis
Piezoelectric coefficient
Frequency
Relative dielectric constant
Electromechanical coupling factor
Monoclinic
Morphotropic phase boundary
Pb(Mg1/3~2/3)03
Pb(Mgll3Nb2/3)0.65Ti0.3503
PbTi03
Pb(Znll3Nb2/3)03
PbZrl-,TiXO3
Rhombohedra1
Tetragonal
Curie temperature
Eutectic temperature
Extrapolated onset melting temperature
Extrapolated onset solidifying temperature
Extrapolated end melting temperature
Extrapolated end solidifying temperature
Thermogravimetry
Peak melting temperature
Peak solidifying temperature
X-ray diffraction
xii
Chapter 1 General Introduction
Lead magnesium niobate Pb(Mg113Nb213) (abbreviated as PMN) and its solid
solutions with lead titanate PbTi03 (abbreviated as PT) belong to the ferroelectric
materials farnily.['l Ferroelectric materials have been used as electromechanical
transducers for undersea communication, medical ultrasound imaging, vibration control
and actuators for more than 50 years. [2-41
1.1 Ferroelectric Materials
A ferroelectric material is the material that has a reversible spontaneous
polarization P, by an external electric field.14' An example is PbTi03. Its spontaneous
polarization in a certain temperature range can be visualized as negative and positive ions
as shown in Figure 1.1."' PbTi03 crystallizes in the perovskite structure. 02- and the
larger cation pb2' form a "close paclung" array with the layers parallel to the { I l l )
planes. The smaller cation ~ i ~ ' occupies an octahedral site. While PbTi03 is in the
tetragonal phase, the ~ i ~ ' ion, slightly too small for its octahedral site, is displaced from
its octahedral centre by about 0.30 A relative to its anionic neighbours. pb2+ also moves
by 0.47A in the same direction as ~ i ~ ' does. Therefore, the centre of the positive charge
does not coincide with the centre of the negative charge, giving rise to a spontaneous
polarization, which can be reversed by the application of an electric field of the opposite
polarity.
Pigure 1.1 Perovskite structure.
A = larger cation (e.g., pb2+), occupies the comer of the cubic;
B = smaller cation (e.g., ~ i ~ ' ) , occupies the centre of the octahedral site formed by 02-;
0 = oxygen ion, is in the face centre of the cubic;
0 and the larger cation A form a "close packing" array (Face Centre Cubic) with the close
packing layers parallel to the (1 1 1 ) planes.
Ferroelectric materials usually exhibit good piezoelectric, dielectric and
electromechanical properties. These ferroelectric and related properties are defined in
Table 1.1.
Tab
le 1
.1 D
efin
itio
ns o
f so
me
phys
ical
qua
ntit
ies
mea
suri
ng th
e re
late
d fe
rroe
lect
ric
prop
erti
es
Phy
sica
l Q
uant
itie
s
elat
ive
,ele
ctri
c In
stan
t (o
r ie
lect
ric
mta
nt)
iezo
elec
tric
)e
ffic
ient
lect
ro-
~ech
anic
al
>up
ling
fact
or
urie
m
pera
ture
Sym
bol
Uni
t
No
unit
Def
init
ion
-
--
The
rat
io b
etw
een
the
char
ge s
tore
d on
tw
o el
ectr
odes
sep
arat
ed b
y a
feno
elec
tric
mat
eria
l an
d th
e ch
arge
sto
red
on
a se
t of
id
enti
cal
elec
trod
es s
epar
ated
by
the
vacu
um.
The
fir
st s
ubsc
ript
ind
icat
es t
he
dire
ctio
n of
the
die
lect
ric
disp
lace
men
t an
d th
e se
cond
ind
icat
es t
he
dire
ctio
n of
the
ele
ctri
c fi
eld
(at d
irec
tion
3).
The
rat
io o
f th
e di
elec
tric
dis
plac
emen
t (c
harg
e Q
per
uni
t ar
ea)
prod
uced
by
the
piez
oele
ctri
c ef
fect
and
the
str
ess
appl
ied
at s
ame
dire
ctio
n. T
he f
irst
sub
scri
pt i
ndic
ates
the
dir
ecti
on o
f th
e di
elec
tric
di
spla
cem
ent a
nd th
e se
cond
indi
cate
s th
e di
rect
ion
of t
he s
tres
s.
The
squ
are
root
of
the
frac
tion
of
mec
hani
cal e
nerg
y (E
m) c
onve
rted
to
elec
tric
al e
nerg
y (E
,) in
eac
h cy
cle,
or
vice
ver
sa. T
he f
irst
sub
scri
pt
indi
cate
s th
e di
rect
ion
of t
he e
lect
ric
fiel
d an
d th
e se
cond
indi
cate
s th
e di
rect
ion
of t
he m
echa
nica
l str
ess.
Pha
se tr
ansi
tion
tem
pera
ture
from
a f
erro
elec
tric
sta
te to
a p
arae
lect
ric
stat
e or
vic
e ve
rsa.
* PC
- pic
0 (1
0-12
) cou
lom
bs, N
- N
ewto
n
1.2 Development of Ferroelectric Materials
Since the discovery of ferroelectric BaTi03 in the early 1940's, a large series of
new ferroelectric materials have been developed.['-4, 61 In general, as electromechanical
transducer materials, they should have a high dielectric constant (K33), a high
piezoelectric coefficient (d33) and a large electromechanical coupling factor (k33).
Increasing these properties became the driving force for the development of new
ferroelectric materials over the past 60 years. Table 1.2 summarizes the historical
performance and evolution of different ferroelectric materials. Figure 1.2 presents the
improvement of the piezoelectric coefficient dg3 for piezoelectric materials since 1940's.
Tab
e 1.
2 D
evel
opm
ent o
f som
e fe
rroe
lect
ric
mat
eria
ls r2
-59 '43'
Com
poun
d P
iezo
elec
tric
co
effk
ient
d33
(P
C~
)*
Dis
cove
re
d ye
ar
Ele
ctro
- m
echa
nica
l co
uplin
g fa
ctor
k33
(%
)*
Bin
ary
PbZ
r03-
P
bTi0
3
Die
lect
ric
cons
tant
K
33 a
t R
T*
cera
mic
s*"
Pb(
Mgv
3Nbm
)03
-PbT
i03
cera
mic
s*"
*See
Tab
le 1
.1 fo
r th
e de
fini
tion
s of
the
pro
pert
ies;
1950
's
PM
N-P
T
and
PZ
N-P
T
sing
le
crys
tals
**
1980
's
Ti d
ispl
acem
ent 0
.1 A
B
a di
spla
cem
ent
0.00
5A
Cur
ie
tem
pera
ture
("
C)*
3100
-500
0 -7
00
-73
1997
Ti d
ispl
acem
ent 0
.30
A P
b di
spla
cem
ent 0
.47
A 36
0 M
PB St
ruct
ural
ch
arac
teri
stic
s
5000
- 60
00
>20
00
>90
-1
60
1 M
PB
220
Per
form
ance
lim
itat
ion
75
Low
wor
king
te
mpe
ratu
re
and
tem
pera
ture
st
abil
ity
Fat
igue
and
agi
ng
4
Rel
ativ
ely
low
d3
3 an
d k3
3
Und
er
inve
stig
atio
n
** M
orph
otro
pic
phas
e bo
unda
ry (
MP
B) c
ompo
siti
on.
PIEZOELECTRIC MATERIALS TREND 1800
PZN-PT
Single Crystats pMN-pTd'
Pigure 1.2 Development of the piezoelectric coefficient d33 for ferroelectric
materials [adapted from Ref. 91
Table 1.2 and Figure 1.2 indicate that ferroelectric materials have been developed
from BaTi03, binary PbZrl-,TiX03 and further to ternary and relaxor ferroelectrics, e.g.,
Pb(Mg113Nb213)(1-x~Tix03 (i.e. PMN-PT) and Pb(Znl/3Nb213)1-xTix03 (i.e. PZN-PT). Among
them, Pb(Mgl/3Nb213)(1-xlTix03 and Pb(Znl13Nb213)l-,TiXO3 single crystals exhibit the
highest ferroelectric properties so far. As Pb(Znl/3Nb2/3)1.xTix03 system has been studied
[lo-111 previously by our group, this work is focused on the PMN-PT system.
1.3 (l-~)Pb(Mg~~~Nb~~~)O~-xPbTi0~ (PMN-PT) Solid Solutions
Previous studies on the PMN-PT solid solution^^'.^^^^ suggest that the excellent
ferroelectric properties can be attributed to the properties of PMN and PT themselves as
well as their morphotropic phase boundary (MPB).
The complex perovslute Pb(Mgl~~Nb2/~)03 (i.e. PMN) is a relaxor fenoelectric
with disorder and local rhombohedra1 symmetry. PMN is characterized by a high
dielectric constant (Kmax >15,000 at f = 1 H z ) , low diffuse phase transition temperature
(Tmax -8 "C at f= kHz) and strong frequency dispersion in the dielectric behaviour. [12-131
In the B site (See Figure 1.1) of Pb(Mg1/3Nb2/3)03, there are two cations of different
valence, M ~ ~ ' and ~ b ~ + . The molar ratio of M~~~ to ~ b " macroscopically is 1:2, but
locally is in 1:l order with a domain size of 2 to 5 nm[23"41. These short-range ordered
domains form an array of clusters and spread inside a disordered matrix, which are
5+ . positively charged (Nb -nch) in order to balance the local negative charge rich).
The self-assembled orderedldisordered nano-structures and the formation of the local
polar domains attribute to the very high dielectric and relaxing properties[19's-161. On the
other hand, PbTi03 (i.e. PT) is a normal ferroelectric with tetragonal phase. It exhibits a
high dielectric constant = 8000 at f = 1kHz and at T,) and an abrupt high phase
transition at Tc = 490 OC.''~] Because of the similar perovslute structures and ion radii
( r M F = 0.78 A, r~?=0.68 A, and rT? = 0.69 A)['], PMN and PT can form solid
solutions (1-x)PMN-xPT (0 I x I 1). These solid solutions exhibit excellent
electromechanical properties with an adjustable para-Iferroelectric phase transition
temperatures to suit a broad range of applications.
It was found that the (1-x)PMN-xPT solid solutions show a nearly vertical
(independent of composition) morphotropic phase boundary (MPB), separating the
tetragonal and rhombohedral phases. The piezoelectric properties around MPB are
enhanced, especially in the single crystal form. These materials exhibit high dielectric
constants (K33 > 5,000 at room temperature), high piezoelectric coefficients (d33 > 2,000
pC/N), and large electromechanical couple factors (k33 > 90%).
The MPB was initially believed to separate the rhombohedral and the tetragonal
phases for PbZr03-PbTi03 and Pb(B'B7')O3-PT (B'= zn2+, B"= ~ b " , etc.)
systems. However, a monoclinic phase in PbZr03-PbTi03 (i.e. PZT)['~] and an
orthorhombic phase in PbZn113Nb21303-PbTi03 (i.e. PZN-PT) "" around the MPB were
recently discovered. This discovery led us to question whether there would also be a
monoclinic or orthorhombic phase in the PMN-PT system since the PMN-PT system has
a similar structure to PZT and PZN-PT. Therefore in this work, we study the phase
structures of (1-x)PMN-xPT system around MPB (0.30 < x < 0.39) to verify the existence
of such a new phase.
8
Since the single crystal form can achieve the highest ferroelectric performance
(See Figure 1.2), more studies are focused on the crystal growth of the (1-x)PMN-xPT
solid solutions (See Section 3.1 for detailed discussion). The PMN-PT single crystals can
be grown from the pure melt. However, there are two concerns during the crystal growth.
First, there are no systematic valid melting point data available for the PMN-PT system.
Therefore, the crystal growth results were often not reproducible.[191 Second, a phase
segregation between PMN and PT usually takes place during the crystal growth.[s1 This
results in the fluctuation of ~i~'-concentration in the grown PMN-PT crystals, which in
turn affects the piezoelectric properties of the single crystal. In order to accurately control
the crystal growth, it is desirable to know the high temperature phase diagram of the (1-
x)PMN-xPT system.
The flux method is commonly used for the crystal growth of the (1-x)PMN-xPT
system. In this method, PbO is usually selected as the Knowing the high
temperature phase diagram of the PMN-PT-PbO system will be helpful for determining
the optimum temperature and flux amount for the crystal growth.
1.4 Objectives of This Work
The goals of this research are
1) To investigate the phase symmetry and establish the phase diagram of
(1-x)PMN-xPT system in the vicinity of the MPB at low temperature;
2) To establish the high temperature phase diagram for the (1-x)PMN-xPT
system (0 5 x < 1);
3) To establish the high temperature phase diagram for the (1-y)(0.65PMN-
0.35PT)-yPbO (0 I y I 1 in weight fraction) system. 0.65PMN-0.35PT is a
MPB composition.
Chapter 2 deals with the low temperature phase diagram of the (1-x)PMN-xPT
system around the MPB. The powder samples for x = 0.30, 0.31, 0.33, 0.35, 0.37 and
0.39 mole fraction will be synthesized at 900 OC in order to form solid solutions. After
that, the powder samples of the above compositions will be pressed into pellets and
sintered at 1200 OC to form ceramics. The samples will then be investigated by means of
high-resolution synchrotron x-ray diffraction at the temperatures between 20 to 500 K to
obtain the phase symmetry around the MPB and to calculate the unit cell parameters for
each symmetry. From these results, the phase structure will be determined and a low
temperature phase diagram for the (I-x)PMN-xPT system in the vicinity of MPB will be
constructed.
Chapter 3 reports the high temperature phase diagram of the (I-x)PMN-xPT
solid solutions. The powder samples for x = 0, 0.1, 0.2, 0.3, 0.35, 0.4, 0.5, 0.6, 0.7, 0.75,
0.8, 0.9 and 1.0 mole fractions will be synthesized at 950 OC to form the solid solutions.
The samples will be further studied by the differential thermal analysis (DTA) to obtain
the melting and solidifying points for each composition. During the DTA measurements,
the powder samples will be sealed in the platinum tubes to avoid the evaporation of PbO.
Based on the high temperature thermodynamic properties, the phase diagram of (1-
x)PMN-xPT solid solutions at high temperatures will be established.
Chapter 4 studies the high temperature phase diagram of PMNT65135-Pb0
system. PMNT65135 [0.65Pb(Mg113Nb213)03-0.35PbTi03] is a MPB composition, and
PbO is the flux used for the crystal growth. PMNT65135 powder will be synthesized at
950 "C to form PMNT65135 solid solution. After that, the powder of
(1-y)PMNT65/35-yPb0, 01 y 5 1, y varying at 0.1 weight fraction, will be prepared and
sealed in the platinum tubes. DTA will be further used to systematically investigate the
meltinglsolidifying properties of PMNT65135-Pb0 system and to establish the pseudo-
binary phase diagram of the (1-y)PMNT65/35-yPb0 system.
The analytical tools used and their intended functions are summarized in Table
1.3.
Table 1.3 Summary of the analytical tools and their intended functions
DTA Systems
Low temperature Formation of the Crystal symmetry Not applicable
PMN-PT at MPB perovskite phase
Conventional XRD
1.5 References
[I]. 2.-G. Ye, Key Eng. Mater. 81, 155 (1998).
High resolution
synchrotron XRD
High temperature PMN-PT
High temperature PMNT6513 5 - PbO
Formation of the pure perovskite phase
Formation of the pure perovskite phase
Not applicable
Not applicable
Melting and solidifying
temperatures
Melting and solidifying
temperatures
[2] Y. Yamashita, Y. Hosono, K. Harada, and N. Yasuda, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 49(2), 184 (2002).
[3] S-E. Park and T.R. Shrout, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 44(5), 1 140 (1997).
[4] Y.-H. Xu, Ferroelectric Materials and Their Application, North-Hollard, Netherlands (1991), Chapter 3.
[5] Y.-H Xu, Ferroelectric and Piezoelectric Materials, Scientific Press, Beijing (1978), Chapter 5.
[6] B. Jaffe, W. R. Cook Jr and H. Jaffe, Piezoelectric Ceramics, Academic Press, London, (1971), Chapter 1.
[7] J. Kelly, M. Leonard, C. Tantigate and A. Safari, J. Am. Ceram. Soc. 80(4), 957 (1 997).
[8] H.-S. Luo, G.-Sh. Xu, H. Xu, P.-Ch. Wang and Zh.-W. Yin, Jpn. J Appl. Phys. 39, 5581 (2000).
[9] S. Saitoh, T. K. Bayashi, S. Shimanuki and Y. Yamashita, Proceedings of SPlE 3037,22 (1997).
[lo] L. Zhang, Master Thesis, Synthesis and Characterization of Relaxor- Based Piezo- and Ferroelectric (l-~)Pb(Zn~,~Nb~,3)03-xPbTiO~ [PZN-PT] & (l-~)Pb(Mg~/~Nb~~)O~-xPbTi03 [PMN-PT], Simon Fraser University (2000), Chapter 3.
[11] M. Dong and Z.-G. Ye, Jpn. J. Appl. Phys. 40,4604 (2001).
[12] Z.-G. Ye and M. Dong, J. Appl. Phys. 187,2312 (2000).
[13] Y. Yamashita, Am. Ceram. Soc. Bull. 73,74 (1994).
[14] L. E. Cross, Ferroelectrics 76,241 (1987).
[15] L. E. Cross, Ferroelectrics 151,305 (1994).
[16] S. M. Gupta and D. Viehland, J. Amer. Ceram. Soc. 80,477 (1997).
[17] B. Noheda, D.E. Cox, G. Shirane, R. Guo, B. Jones, and L.E. Cross, Phys. Rev. B 63,O 14 103 (2000).
[18] D. La-Orauttapong, B. Noheda, 2.-G. Ye, P. M. Gehring, J. Toulouse, D. E. Cox, and G. Shirane, Phys. Rev. B 65, 144101 (2002).
[19] Z.-G. Ye, M. Dong and Y. Yamashita, J. Cryst. Growth 211, 247 (2000).
[20] Y. Yamashita and S. Shimanuki, Mater. Res. Bull. 31, 887 (1996).
[21] 2.-G. Ye, P. Tissot and H. Schmid, Mater. Res. Bull. 25,739 (1990).
[22] M. Dong and Z.-G. Ye, J. Cryst. Growth 209, 81 (2000).
[23] J. Chen, H. M. Chan and M. P. Harmer, J. Am. Ceram. Soc. 72,593 (1989)
[24] C. A. Randall, A. D. Hilton, D. J. Barber and T. R. Shrout, J. Mater. Sci. 25, 3461 (1 990)
Chapter 2 Low Temperature Phase Diagram of (1-x)PMN-xPT
Solid Solutions around the Morphotropic Phase Boundary
2.1 Introduction
Pb(Mg,~~Nb2/~)0~ (designated as PMN) is a typical relaxor ferroelectric with
disorder and local rhombohedral (R) symmetry. PbTi03 (designated as PT) is a normal
ferroelectric with tetragonal (T) symmetry. Because they have similar perovskite
structures, PMN and PT can form a series of solid solutions (1-x)PMN-xPT (0 5 x 5 1).
These solid solutions combine both the characteristics of the relaxor ferroelectric PMN
and ferroelectric PT, exhibiting high piezoelectric properties. Especially, around the
morphotropic phase boundary (MFB) (x = 0.30 - 0.35)[11, the ceramics of these solid
solutions show high dielectric constant (K33 - 5000 at room temperature), high
piezoelectric coefficient (d33 - 700 pC/N) and large electromechanical coupling factor
(k33 - 73 %)[2-61. These properties make them the best candidate materials for
electromechanical transducers.
2.1.1 The Structure of Relaxor Ferroelectrics around the Morphotropic Phase
Boundary
The excellent piezoelectric properties of (1-x)PMN-xPT are related to the MPB,
which separates the rhombohedral (R) phase from the tetragonal (T) phase as illustrated
mixture of the two adjacent rhombohedra1 and tetragonal phases, which was used to
explain the high piezoelectric effects of these materials.
Figure 2.1 Original low temperature phase diagram of the (1-x)PMN-xPT solid
solutions (Adapted from Ref. 1)
Table 2.1 Phase symmetry of some ferroelectrics around the morphotropic phase
boundary
Composition Phase around Composition range Techniques used
I MPB I of the new phases
PbZrl-,Ti,O3
( 1 -x)PZN-xPT
Notes:
(1 -x)PMN-xPT
R - Rhombohedral, M- Monoclinic, T - Tetragonal, 0 - Orthorhombic,
R+M+T
R+O+T
TBD - To be determined.
Some recent studies have revealed the existence of a new phase between the two
adjacent ferroelectric phases at the MPB (See Table 2.1). Noheda et al[7-81 revisited the
ceramic samples of PbZrl-,Ti,03 (PZT) system with the composition 0.42 5 x 1 0.52
At 20 K, 0.46 5 x 5 0.51 mole fraction (x narrows as the temperature increases) Orthorhombic range 0.08 < x < 0.1 1 mole fraction
Synchrotron XRD
I
(mole fraction) by high-resolution synchrotron x-ray powder diffraction measurements.
Synchrotron XRD
Synchrotron XRD
R+TBD+T
They found that a low symmetry monoclinic phase exists between the rhombohedra1 and
TBD (this work)
tetragonal phases. At 20 K, the monoclinic phase is stable in the range 0.46 5 x 5 0.51
(mole fraction), and this range becomes narrower as the temperature increases. In the (1-
x)PZN-xPT (0 5 x 5 1) system, synchrotron x-ray diffraction experiments revealed that
16
around MPB, an orthorhombic phase exists in a narrow composition region (0.08 < x c
0.11 mole fraction) between the rhombohedral and tetragonal phases. [9- 101
Since the monoclinic and orthorhombic phases were discovered near the MPB in
PZT and (1-x)PZN-xPT systems, new studies were performed on the (1-x)PMN-xPT
system recently as these three systems have a similar perovskite structure. Under the
polarizing microscope at room temperature, monoclinic domains were found on
0.67PMN-0.33PT single crystals.[111 With the high-resolution synchrotron x-ray
diffraction, 0.65PMN-0.35PT single crystal, poled along the [001] direction under an
electric field of 43 kV/cm, appears to have monoclinic symmetry.[121 With the
conventional x-ray diffraction, monoclinic phase was found in the synthesized 0.66PMN-
0.34PT powder at room temperature.[131 All these results suggested that the symmetry of
(1-x)PMN-xPT around the MPB should be different from the original symmetry (A
mixture of the two adjacent rhombohedral and tetragonal phases, see Figure 2.1).
Therefore, further systematic studies of the crystal structure around this region are
required to confirm the existence of a monoclinic phase and to define a stable region for
this new phase.
2.1.2 Synchrotron X-ray Diffraction
Synchrotron XRD was used in this experiment as a major technique to determine
the phase symmetry of the PMN-PT solid solutions around the MPB.
Synchrotron radiation is an electromagnetic radiation emitted by electrons moving
on circular orbits at the velocity close to the speed of light (2.998 x 10' rn~sec).[ '~~ While
the electrons travel along the orbits, a series of magnets are used to bend the path of the
17
electrons into a circular shape (Figure 2.2). As the electrons pass these "bending"
magnets, the path of the electrons is deflected and electrons emit intense beams of light,
known as synchrotron radiations, which form a continuous spectrum from infrared (- 1
mm) to X-ray (0.1 A) region.
Compared with conventional x-ray, the intensity of synchrotron x-ray is hundreds
of thousands of times higher and the angular resolution is one order of magnitude better
(0.005-0.01" for synchrotron XRD and 0.05" for conventional XRD).''~] Therefore,
synchrotron XRD can detect more details on local structure of materials than
conventional XRD, as shown in Figure 2.3. This figure shows the cubic (1 11) diffraction
patterns of 0.70PMN-0.30PT obtained from the conventional XRD and synchrotron XRD
respectively. In Figure 2.3 (a), only one single peak was detected around the cubic (1 11)
reflection by conventional XRD. However, two overlapping peaks were clearly detected
in Figure 2.3 (b) using synchrotron XRD. At room temperature, 0.70PMN-0.30PT has
rhombohedra1 symmetry with lattice angles a = P = y = 89.89". Since the lattice angles
are not equal to 90•‹, the interplanar d-spacing is different for (1 11) plane set and (1-1 1)
plane set. Because the lattice angles are very close to 90•‹, it is difficult to distinguish
(111) and (1-1 1) reflections by conventional XRD. Therefore, in order to obtain the
detailed phase symmetry of PMN-PT system around MPB, the high-resolution
synchrotron XRD was used in this work.
The purpose of this study is to determine the low temperature phase symmetry of
(1-x)PMN-xPT system in the vicinity of MPB with the high resolution synchrotron XRD
and to construct the low temperature phase diagram within the composition range 0.30 5
x 1 0.39 mole fraction.
Figure 2.2 Synchrotron radiation
(a) Conventional x-ray diffraction (b) Synchrotron x-ray diffraction
Figure 2.3 The cubic (111) reflection obtained from conventional x-ray diffraction
and synchrotron x-ray diffraction. Synchrotron XRD can distinguish peaks of (11 1)
and (1-ll), but conventional x-ray diffraction can not. [Figure 2.3 (b), by permission of
B. Noheda].
2.2 Experimental
2.2.1 Preparation of Solid Solutions
In order to prepare the perovslute phase of the solid solutions of (I-x)PMN-xPT, a
two-step columbite precursor method[161 was used to avoid the formation of a pyrochlore
phase (of Pb3Nb4013-type). The pyrochlore phase is thermodynamically more stable but
unfavorable for the ferroelectric properties. The first step is to form a columbite precursor
of magnesium niobate (MgNb206) by reacting MgO and Nb205 at 1100 O C . In the second
20
step, MgNb2o6 was further mixed with PbO and Ti02 at 900 OC to form the
stoichiometric (1-x)PMN-xPT solid solutions. Detailed procedures are described below.
Step 1: Formation of MgNbz06 Precursor
Starting chemicals, Nb205 (H.C Stark, 99.9%) and MgO (Koujando, 99.9%)
powders, were dried at 110 OC for 2 hours before weighing. A mixture of MgO and
Nb2O5 containing a 15.5 wt% excess of MgO over the 1:1 stoichiometric ratio was
weighed. The excess amount of MgO was added to make up the thermal gravimetric loss
of H20 and C02, which were initially adsorbed in commercial MgO powder. Figure 2.4
shows the thermal gravitation loss of the commercial MgO at about 366 OC. After
weighing, the mixture of MgO and Nb205 was ground in the presence of ethanol for 1
hour, cold-pressed into pellets and calcined at 1100 OC for 12 hours to form the pure
columbite precursor phase of MgNb206 based on equation (2-1). Conventional x-ray
powder diffractometer was used to check the formation of the MgNb206 phase.
1 100"C, 12 hrs MgO + Nb205 - MgNb20s
Step 2: Preparation of the (1-x) PMN-x PT solid solutions
The columbite precursor (MgNb206) was then mixed with PbO (GFS, 99.99%)
and Ti02 (Japan. Institute, 99.9%), according to equation (2-2). An excess amount of
PbO (2 wt%) was added to compensate the PbO loss during the subsequent calcinations
and sintering. Samples were thoroughly ground in ethanol, cold-pressed into pellets, and
synthesized at 900 OC for 4 hours in an open platinum crucible to form the solid
21
solutions. After synthesis, XRD was carried out to detect the presence of any unfavorable
pyrochlore phase (of Pb3Nb4OI3) and the formation of the favorable perovskite solid
solutions for each composition.
900•‹C, 4 hrs [(I-x)/3]MgNb206 + PbO + xTi02 ,-* Pb(Mg113Nb213)1-~Ti~03
(x = 0.30,0.31, 0.33, 0.35, 0.37 and 0.39 mole fractions)
0 200 400 600 800 1000
V•‹C) Fgure 2.4 Thermogravimetry/differential thermal analysis for the commercial MgO.
2.2.2 Preparation of Ceramic Samples
Ceramic samples were used for the study of synchrotron x-ray diffraction. For the
(1-x)PMN-xPT (or PMN-xPT) ceramic samples (x = 0.30, 0.31, 0.33, 0.35, 0.37 and
0.39), the calcined powder (from Step 2 of Section 2.2.1) was ground for 1 hour, mixed
with a binding agent [Polyvinyl alcohol (PVA)] and cold-pressed into pellets of 3 mm in
thickness and 15 mm in diameter. The pellets were first heated up to 650 "C on an
alumina plate to drive off the PVA, and then sintered at 1200-1230 "C for 4 hours in a
sealed alumina crucible with PbO-enriched atmosphere to form high-density ceramics.
The surface of the ceramic pellets were finally polished with 1 pm diamond paste and
ultrasonically cleaned before x-ray diffraction experiments.
2.2.3 Conventional X-ray Diffraction Measurements
Conventional X-ray diffraction (XRD) measurements were performed on a
Philips powder diffractometer (Cu Ka, h = 1.5418 A) at SFU. The angular resolution on
the 28 scale was 0.05". The scan-step was set at 0.05" intervals.
XRD was carried on the MgNb206 precursor compound (From Step 1) to verify
the formation of the columbite phase. XRD was also carried on the powder of
(I-x)PMN-xPT solid solution and the ceramic samples at room temperature to verify the
formation of the perovskite phase.
2.2.4 Synchrotron X-ray Diffraction Measurements
Synchrotron x-ray diffraction was carried out on the (1-x)PMN-xPT ceramic
samples (from Section 2.2.2) at temperatures T = 20 K, 300 K, 350 K, 375 K, 400 K, 475
K and 500 K to study the phase symmetry around the MPB.
The diffraction measurements were performed on the beam line X7A at the
Brookhaven National Synchrotron Light Source (BNSLS), in collaboration with Drs. B.
Noheda, G. Shirane and D. E. Cox. A Si (111) double-crystal monochromator was used
to provide an incident beam with a wavelength 0.70040A. A Ge (220) analyzer and a
scintillation detector were mounted in the diffracted beam, giving an instrumental angular
resolution [Full Width at Half Maximum (FWHM)] of about 0.005-0.01" on the 20 scale,
an order of magnitude better than the angular resolution of conventional XRD (0.05").
For temperature dependence measurements, the ceramic powder samples were
prepared by chopping out small fragments from the ceramic pellets, grinding them in an
agate mortar with acetone and loading them in a 0.2-mm-diameter capillary. A closed-
cycle He cryostat was used for the low temperature measurements and the temperature
accuracy was 4 -2K around 20 K. A wire-wound BN tube furnace was used for the
measurements above room temperature. The temperature accuracy of the furnace is +/-I0
K between 300 and 500 K. The step-scans were set at 0.005 to 0.01" intervals. During
data collection, the samples were either rotated at about 1 Hz or rocked over 2"-3" to
reduce the effect of the preferred orientation. The scans were carried out over narrow
angular regions centred at about the six cubic reflections (loo), (1 lo), (1 1 I), (200), (220)
and (222), in order to determine the crystal symmetry and related lattice parameters
within the limits of the instrumental resolution.
During the data analysis, the individual reflection profile was fitted by the least-
square method to a pseudo-Voigt function, with intensity, peak position, peak-width
(FWHM) and mixing parameter as variables to determine the phase symmetry and the
lattice parameters. The definition of the pseudo-Voigt function can be found in the
Appendix.
2.3 Results and Discussion
2.3.1 Conventional X-ray Diffraction
Conventional XRD was used to make sure that there was only perovskite phase
and no pyrochrole phase in the PMN-xPT ceramic samples. XRD angle 28 was selected
from 28 to 35', which covered the strongest peak (29.3") of pyrochlore phase of
Pb3Nb4OI3-type. Figure 2.5 shows a segment of the XRD spectrum for PMN-39PT solid
solution. It can be seen that no pyrochlore phase is detectable and a pure perovskite phase
is confirmed.
P M N - 3 9 P T
strongest peak
28 29 30 31 32 33 34 35
28 (deg) Figure 2.5 A segment of conventional x-ray diffraction spectrum for a PMN-39PT
ceramic sample, showing a pure perovskite phase with no presence of the pyrochlore
phase.
2.3.2 Synchrotron X-ray Diffraction
2.3.2.1 Analytical Steps of Synchrotron X-ray Diffraction Patterns
The analysis of the synchrotron XRD diffraction patterns follows the five steps
listed below:
1) Original diffraction data points (shown as solid circles in Figure 2.6) were
obtained directly from the high-resolution synchrotron XRD.
2) The data was fitted by the pseudo-Voigt (P-V) function (see Appendix for the
definition of the pseudo-Voigt function).
3) The initial 28 values for each peak, calculated from a proposed phase symmetry
and lattice parameters, were put into the graph and the least-square method was
used to compare the original diffraction data and the fitting profiles.
4) If there were residual intensities that cannot be fitted, other peaks were added at
that position. All peak positions have to be matched with the lattice parameters of
the proposed phase symmetry.
5) From the peak positions, possible crystal symmetries were identified, i.e.,
Rhombohedral, Tetragonal andlor Monoclinic.
2.3.2.2 Composition Effect on the Synchrotron X-ray Diffraction Patterns
The XRD profiles around the cubic (1 1 I), (200) and (220) reflections for PMN-
30PT, PMN-3lPT, PMN-33PT and PMN39PT at 300 K are presented in Figure 2.6.
Rhombohedral R3m
Monoclinic Pm + Rhombohedra1
Monoclinic Pm + Tetragonal
Tetragona P4mm
Figure 2.6 Synchrotron x-ray diffraction patterns of selected regions at 300 K with
0.70040 A wavelength for a) PMN-30PT, b) PMN31PT, c) PMN-33PT and d) PMN-
39PT. The solid lines are the least-squares fits to the data points and the vertical arrows
represent the peak positions obtained from the fits for different phases, R, T, or M
Figure 2.6 shows that around the cubic (11 I), (200), and (220) reflections, the
peak positions and shapes for different compositions are different. For example, at cubic
(200) reflection, PMN-30PT has only one single peak at 20 = 20.05" [See Figure 2.6 (a)].
While PMN-31PT and PMN-33PT have several overlapping peaks between 20 = 19.8"
and 20.2" [See Figure 2.6 (b) and (c)]. PMN-39PT has two separate single peaks at 28 =
19.85" and 20.15", respectively [See Figure 2.6 (d)]. These results indicate that the
crystal symmetry changes from rhombohedral to tetragonal through an intermediate
phase as the composition varies through the MPB.
Following the steps of analysis mentioned in Section 2.3.2.1, we conclude that
PMlN-30PT is a pure rhombohedral phase and PMN-39PT is a pure tetragonal phase.
On the other hand, PMN-31PT and PMN-33PT show considerably more
complicated diffraction patterns. Various combinations of rhombohedral phase (R),
tetragonal phase (T), and monoclinic phase (M) were considered for the identification of
the peaks. The results for PMN-3 1PT and PMN-33PT are discussed as below:
(i) PMN-31PT [See Figure 2.6 (b)]: For cubic (111) and (220) reflections, both the
monoclinic and orthorhombic phases are found to fit well since the diffraction peaks of
these two phases are very close to each other. However, the cubic (200) reflection
pattern is different for the monoclinic and orthorhombic phases at this position. A
monoclinic phase has three overlapped peaks with roughly the same intensity ratio,
while the orthorhombic phase has two overlapped peaks with a 2: 1 intensity ratio. The
diffraction peaks in Figure 2.6 (b) could be fitted by three overlapped monoclinic
peaks. Together with other reflections [e.g. (1 1 l), (220) etc.], the monoclinic phase is
assigned to the PMN-31PT composition. Besides, several dotted arrows indicated in
Figure 2.6 (b) around the cubic ( I l l ) , (200) and (220) reflections can be accounted for
by the presence of the rhombohedral phase, with an estimated volume fraction of about
30%. The calculation of the volume fraction is based on the intensity ratio between the
rhombohedra1 and monoclinic phases.
(ii) PMN-33PT [See Figure 2.6 (c)]: The monoclinic phase in PMN-33PT is found to
account well for most of the peaks. Compared to the monoclinic phase of PMN-31PT
[Figure 2.6 (b)], there is a larger split of the three peaks in the cubic (200) reflection for
PMN-33PT, corresponding to a monoclinic distortion with a greater difference between
a, and c, (a, and c, are two of the three unit cell parameters of the monoclinic phase).
Several dashed arrows shown in Figure 2.6 (c), especially the one at low angle shoulder
of cubic (200) reflection, can be matched with the presence of a tetragonal phase with a
volume fraction of about 25%.
Table 2.2 summaries the results of phase analysis from synchrotron XRD data for
PMN-xPT at 300 K.
Table 2.2 Summary of phase symmetries and lattice parameters at 300 K for
(1-x)PMN-xPT around the morphotropic phase boundary
Note:
x no1 %)
30
31
33
35
37
39
* R - Rhombohedral, M - Monoclinic, 0 - Orthorhombic, T - Tetragonal. The lattice
parameters of monoclinic phase and orthorhombic phase can not be determined
respectively at this time since the peak intensities are weak.
** a, b and c are the lattice parameters of the unit cell (experimental error + 0.002 A). a
(between b and c), P (between a and c) and y (between a and b) are the three angles of the
unite cell (experimental error + 0.02").
*** N/A - Not available. The lattice parameters of the M phase for PMN-37PT could not
be determined with accuracy at this time because of the peak overlapping.
Sym.
R*
R*
M*
M*
T*
M+O*
T*
M*
T*
T*
Vol (%)
100
3 0
70
7 5
25
35
65
20
80
100
a (A)**
4.017
4.017
4.01 8
4.019
4.005
4.018
4.000
N/A***
3.998
3.994
b (A)**
4.017
4.017
4.007
4.006
4.005
4.000
4.000
N/A
3.998
3.994
c (A)**
4.017
4.017
4.026
4.032
4.046
4.035
4.044
N/A
4.049
4.047
a = y p)**
89.89
89.89
90.00
90.00
90.00
90.00
90.00
N/A
90.00
90.00
p o**
89.89
89.89
90.15
90.19
90.00
90.12
90.00
NIA
90.00
90.00
It can be seen that with x increasing from 30 to 39 mol%, the phase symmetry
changes from a pure rhombohedral phase, to a mixture of monoclinic and rhombohedral
phases, then to a combination of monoclinic and tetragonal phases, and finally to a pure
tetragonal phase. For 31 5 x 5 37 mol%, the monoclinic phase appears first as the
majority phase (70 vol% of M at 31 mol% of PT), and then becomes a minority phase
(20 vol% of M at 37 mol% of PT).
2.3.2.3 Temperature Effect on the Crystal Structures
In additional to the results of the temperature at 300 K, the synchrotron XRD was
also performed at temperatures of 20 K, 325 K, 350 K, 375 K, 400 K, 425 K, 450 K and
500 K.
The diffraction profiles of PMN-35PT around the cubic (200), (220) and (222)
reflections at T = 20 K, 400 K and 450 K are presented in Figure 2.7. The figure shows
that only one peak appears around each reflection at 450 K (See the red curves in Figure
2.7), indicating a cubic symmetry of PMN-35PT. At 400 K (See the blue curves in Figure
2.7), there are two peaks around the cubic (200) and (220) reflections respectively,
indicating the tetragonal symmetry.
Figure 2.7 Synchrotron x-ray diffraction patterns of PMN-35PT at 450 K, 400 K
and 20 K in the selected regions. The inset shows the data points, the fitting curve and
the peak positions obtained from the fitting around the cubic (220) at 20 K.
Compared with the synchrotron XRD profiles at 400 K and 450 K, the diffraction
patterns at 20 K (See the black curves in Figure 2.7) are relatively complicated. In the
cubic (200) profile, the high angle peak (corresponds to the small lattice parameter - b,)
is sharp. In contrast, the intensity in the lower angle region is relatively small and the
peaks become broad. It is difficult to fit the broad peaks. Fortunately, the (hhO) and (hhh)
reflections do not show this broadening. The inset of Figure 2.7(b) shows the
experimental data points and the six-peak fit around the cubic (220) reflection at 20 K.
The results indicate the existence of the monoclinic phase (four peaks) and tetragonal
phase (two peaks). However, in other (hhO) profiles of 20 K, there is one unidentified
peak and some significant discrepancies in the intensity ratios. These features can be
accounted for very well by the third orthorhombic (0) phase with 30 % volume fraction.
The lattice parameters calculated based on the diffraction patterns of PMN-35PT at 20 K
are shown in Table 2.3.
Based on the synchrotron x-ray diffraction patterns obtained at different
temperatures, the lattice parameters as a function of temperature for the compositions of
PMN-39PT, PMN-3 lPT, PMN-33PT and PMN37PT are discussed as below:
(i) PMN-39PT (See Figure 2.8) The Curie temperature is defined as a phase transition
temperature from ferroelectric phase to paraelectric phase. The vertical dotted line in
Figure 2.8 shows the Curie temperature (Tc), at which the ferroelectric tetragonal
phase changes to the paraelectric cubic phase upon heating. The Tc value (= 450 K)
obtained from the synchrotron XRD from this work is in good agreement with that
obtained from the dielectric measurements by Noblanc et UZ.[' '~ Above Tc, PMN-39PT
34
is a cubic phase; while below Tc (down to 20 K), PMN-39PT has a tetragonal phase.
At 20 K, the difference between at and ct is about 0.09 A, corresponding to a c/a ratio
(i.e. tetragonality) of 1.022. As the temperature increases, the difference between a,
and c, becomes smaller. At Tc = 450 K, a, and ct merge into one value, corresponding
to the lattice parameter (a,) of the cubic phase.
Figure 2.8 Variation of the lattice parameters as a function of temperature for
PMN-39PT. at (solid circles) and ct (open circles) are the lattice parameters of the
tetragonal unit cell (experimental error + 0.002 A). a, is the lattice parameter of cubic
unite cell (experimental error + 0.002 A). Vertical dotted line indicates the phase
transition from tetragonal to cubic at Tc - 450 K.
(ii) PMN-31PT (See Figure 2.9) The temperature effect on the lattice parameters reveals
a structure evolution from the monoclinic to the tetragonal and then to the cubic
phases. Between 20 and 350 K the minority rhombohedral phase coexists with the
majority monoclinic phase. In order to make the graphs clear, the lattice parameters of
the minority rhombohedral phase are not shown in the graph. P is the angle between
monoclinic axes a, and c,. (P-90•‹), shown on the bottom part of the graph, describes
the deviation of p from 90". At 20 K, the monoclinic lattice parameters a, and c, are
fairly well differentiated. As the temperature increases, a, and c, get closer to each
other. At 350 K, these two lattice parameters can no longer be resolved, as indicated
by the error bars in Figure 2.9. Between 350 K and 375 K, the monoclinic phase
transforms to the tetragonal phase and (P-90") reaches 0". It can be seen that the
variation from b, to a, is continuous at the phase transition, similar to the behaviour
observed in the (1-x)PZN-xPT system.[181 At Tc = 425 K, the tetragonal phase
transforms to the cubic phase. The temperature of Tc is consistent with the reported
value.['71
(iii) PMN-33PT (See Figure 2.10) The temperature effect on the monoclinic lattice
parameters is similar to that of PMN-31PT, except for the larger difference between
the a, and the c,. Between 20 and 320 K, the minority tetragonal phase coexists with
the majority monoclinic phase. In order to make the graphs clear, the lattice
parameters of the minority tetragonal phase is not shown in the graph. Figure 2.10
illustrates that a monoclinic phase transforms to a tetragonal phase between 300 and
325 K, then to the cubic phase between 400 and 425 K. The second temperature range
(between 400 and 425) is consistent with the reported value.r171 The variation of lattice
parameter from b, to a, is continuous at the phase transition from monoclinic to
tetragonal phase.
Figure 2.9 Variation of the lattice parameters of the monoclinic phase as a function
of temperature for PMN-31PT. a,, b, and c, are the lattice parameters of the
monoclinic unit cell. The experimental error of the lattice parameters is + 0.002 8, and the
experimental error of monoclinic angle @ is k 0.02'. The vertical dashed line indicates the
phase transition from the monoclinic to the tetragonal between 350 K and 375 K. The
vertical dotted line represents the phase transition from the tetragonal to the cubic at T, = 425 K.
Figure 2.10 Variation of the lattice parameters of the monoclinic phase as a function
of temperature for PMN-33PT. a,, b, and c, are the lattice parameters of the
monoclinic unit cell (The experimental errors of lattice parameters +. 0.002 A, the
experimental error of monoclinic angle P -i: 0.02"). The vertical dashed line indicates the
phase transition from the monoclinic to the tetragonal at about 320 K. The vertical dotted
line represents the phase transition from the tetragonal to the cubic at Tc =: 400 - 425 K.
(iv) PMN-37PT (See Figure 2.11) The temperature effect on the lattice parameters of
PMN-37PT is shown in Figure 2.11. Between 20 K and about 325 K, the monoclinic
phase coexists with tetragonal phase. The shaded temperature range indicates that the
volume fraction of the monoclinic (or tetragonal) phase gradually decreases (or
increases). At 20 K and 200 K, the volume fraction of the monoclinic phase is 55%.
AT 300 K, the volume fraction of the monoclinic phase decreases to 20%. At 325 K,
the monoclinic phase disappears and only tetragonal phase is found. The vertical
dotted line represents the phase transition from the tetragonal to the cubic between 450
K and 475 K.
The results of phase analysis from synchrotron XRD data for PMN-xPT at 20 K
are summaries in Table 2.3. This Table illustrate that from 30 %PT to 39 %PT, the phase
symmetry of PMN-xPT experiences the phase change from a pure rhombohedral phase,
to a mixture of rhombohedral and monoclinic phases, then to a combination of
monoclinic and tetragonal phases, finally to a pure tetragonal phase. In PMN-35PT, an
orthorhombic phase (a volume fraction of 35 %) mixes with the tetragonal and the
monoclinic phases. For 31 5 x 5 37 mol%, the monoclinic phase appears as a majority
phase (55 vol% up at this composition range). The stability region of the monoclinic
phaseat20Kis31 % _ < x 5 3 7 % .
Figure 2.11 Variation of the lattice parameters of the monoclinic and tetragonal
phases as a function of temperature for PMN-37PT. a,, b, and c, are the lattice
parameters of the monoclinic unit cell. a,, and c, are the lattice parameters of the
tetragonal unit cell. The experimental error of the lattice parameters is & 0.002 A, the
experimental error of monoclinic angle P is + 0.02". The shaded temperature range shows
the volume fraction of the monoclinic (or tetragonal) phase gradually decreases (or
increases). The vertical dotted line represents the phase transition from the tetragonal to
the cubic between 450 K and 475 K.
Table 2.3 Summary of phase symmetries and lattice parameters at 20 K for (1-
x)PMN-xPT around the morphotropic phase boundary
Note:
* R - Rhombohedra1 phase, M - Monoclinic phase, T- Tetragonal phase. 0 -
Orthorhombic phase.
** a, b and c are the lattice parameters of the unit cell (experimental error of lattice
parameter k 0.002 A). a (between b and c), P (between a and c) and y (between a and b)
are the three angles of the unite cell (experimental error of lattice angle + 0.02").
2.3.2.4 Summary of the Composition Effect on the Lattice Parameters
The composition effect on the lattice parameters in the (1-x)PMN-xPT system (x
= 0.30, 0.31, 0.33,0.35, 0.37 and 0.39) at 300 K and 20 K is presented in Figure 2.12 and
Figure 2.13, respectively. Only the lattice parameters of the majority phases are plotted
for clarity. Both figures show the structure evolution from the rhombohedral to the
tetragonal phase via the monoclinic phase.
At 300 K (Figure 2.12), the compounds of x 5 31 % exhibit the rhombohedral
phase. For x 2 35%, the tetragonal phase is found with a strain ratio (or tetragonality)
varying from ct/at 1.011 at x = 35% to 1.103 at x = 39%. The monoclinic phase range is
31% 5 x 5 35%. Besides, the monoclinic lattice parameters of 66PMN-34PT from Ref.
[13] (open triangle points in Figure 2.12) are in good agreement with our trend.
At 20 K (Figure 2.13), the monoclinic phase is found in the composition range of
31% 5 x 5 37%, which is slightly wider compared with the monoclinic phase range at
300 K. Both Figure 2.12 and Figure 2.13 illustrate the discontinuity of the lattice
parameter changing from the rhombohedral to the monoclinic phase and from the
monoclinic to the tetragonal phase. These indicate the abrupt phase transitions.
Figure 2.12 Variation of the lattice parameters of the majority phases as a function
of PbTiO, concentration at 300 K (the experimental errors of the lattice parameters 5
0.002 A, the experimental errors of the lattice angles 5 0.029. Solid black circles are the
lattice parameters obtained from this work and open triangles are the reported data of
P M N - ~ ~ P T . ' ~ ~ ' Two dotted vertical lines indicate the compositions, at which the phase
transitions R -+ M and M -+ T take place.
Figure 2.13 Variation of the lattice parameters of the majority phases as a function
of PbTiO, concentration at 20 K (the experimental errors of lattice parameters + 0.002
A, the experimental errors of lattice angles + 0.02'). Two dotted vertical lines indicate the
compositions at which the phase transitions R -- M and M - T take place.
2.4 Phase Diagram in the Region of the Morphotropic Phase Boundary
Based on the above experimental results and analysis, a new phase diagram for
the (1-x)PMN-xPT around the MPB has been constructed, as shown in Figure 2.14. The
stability region of the monoclinic phase was diagonally shaded. The vertical dash dot line
and the horizontal dash dot arrows indicate the rhombohedral (x 5 32%) or tetragonal (x
2 32%) secondary phases. The solid dots obtained from this work shows the transition
temperatures from ferroelectric to paraelectric cubic phase within the composition 30 % 5
x 5 39 % mole fraction, which are in good agreement with the reported value.[17'
2.5 Conclusions
In conclusion, a new low temperature phase diagram for the (1-x)PMN-xPT solid
solutions in the vicinity of MPB has been proposed, in which the stability region of the
monoclinic phase is found to be 0.31 5 x 5 0.37 mole fraction at temperature range from
20 K to 300 K. From 20 to 500 K, the monoclinic phase changes to tetragonal phase then
to cubic phase. The existence of a secondary phase in this range, either tetragonal or
rhombohedral phase, has been observed in all the MPB compositions. Lattice parameters
are also calculated based on the synchrotron XRD within 0.30 5 x 5 0.39. This phase
diagram provides valuable information for understanding the nature of the MPB.
E
X
Figure 2.14 New phase diagram of (1-x)PMN-xPT solid solutions in the vicinity of
the morphotropic phase boundary deduced from the synchrotron x-ray diffraction
results.
2.6 References
[I] T. R. Shrout, Z. P. Chang, N. Kim, and S. Mar Kgraf, Ferroelctrics Lett. 12, 63 (1990).
[2] X.-W. Zhang and F. Fang, J. Mater. Res. 14(12), 4581 (1999).
[3] S-E. Par K and T. R. Shrout, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 44(5), 1140 (1997).
[4] S-E. Par K and T. R. Shrout, Mater. Res. Innovations 1,20 (1997).
[5] K. Harada, S. Shimanu Ki, T. Kobayashi, S. Saitoh and Y. Yamashita, Key Eng. Mater. 157-158,95 (1999).
46
[6] T. Kobayashi, S. Shimanu Ki, S. Saitoh and Y. Yamashita, Jpn. J. Appl. Phys., Part 1 36,6035 (1997).
[7] B. Noheda, D.E. Cox, G. Shirane, R. Guo, B. Jones, and L. E. Cross, Phys. Rev. B 63,
[8] B. Noheda, J. A. Gonzalo, L.E. Cross, R. Guo, S.-E. Park, D. E. Cox and G. Shirane, Phys. Rev. B 61,8687 (2000).
[9] D. E. Cox, B. Noheda, G. Shirane, Y. Uesu, K. Fujishiro and Y. Yamada, Appl. Phys. Lett. 79,400 (2001).
[lo] D. La-Orauttapong, B. Noheda, Z.-G. Ye, P. M. Gehring, J. Toulouse, D. E. Cox, and G. Shirane, Phys. Rev. B 65, 144101 (2002).
[ l l ] G. Xu, H. Luo, H. Xu, and Z. Yin, Phys. Rev. B 64,020102 (2001).
[12] Z.-G. Ye, B. Noheda, M. Dong, D. Cox, and G. Shirane, Phys Rev. B 64, 184114 (2001).
[13] A. K. Singh and D. Pandey, J. Phys.: Condens. Matter 13, L931 (2001).
[14] C. Kunz, Synchrotron Radiation-Techniques and Applications, Springer-Verlag Berlin Heidelberg, New York (1979), Chapter 1.
[15] Z.-G. Ye, Y.-H. Bing, J. Gao, A. A. Bokov, P. Stephens, B. Noheda and G. Shirane, Phys Rev. B. 67,104104 (2003).
[16] S. L. Swartz and T. R. Shrout, Mater. Res. Bull. 17, 1245 (1982).
[17] 0 . Noblanc, P. Gaucher, and G. Calvarin, J. Appl. Phys. 79,4291 (1996).
[18] B. Noheda, D. E. Cox. G. Shirane, S-E. Park, L. E. Cross and Z. Zhong, Phys. Rev. Lett. 86,3891 (2001).
Chapter 3 High Temperature Phase Diagram of the
(1-x)PMN-xPT Solid Solutions
3.1 Introduction
Relaxor ferroelectrics Pb(Mg113Nb213)03 (PMN) and its solid solutions with
ferroelectrics PbTi03 (designated as PT) have been intensively studied recently because
of their superior dielectric and piezoelectric properties.r1-21 Particularly, in the single
crystal form, PMN-PT crystals have been reported to exhibit very high piezoelectric
coefficient (d33 > 2,000 pC/N), very large electromechanical coupling factor (K33 > 90
%).r2-61 Such excellent performance makes them promising materials for the next
generation electromechanical transducers.
The outstanding performances of PMN-PT single crystals have initiated
investigations on the crystal growth.[71 PMN-PT single crystals can be grown from pure
melt. In 1999, Lee et al. first used the Bridgman technique (one kind of pure melt
method) to grow large PMN single crystal.[*l After that, a number of papers were
published on the Bridgman growth of PMN-PT.[~-"] There are two issues on the crystal
growth from pure melt. First, there are not systematic melting point data for PMN-PT
system available. Therefore, the growth results were often not reproducible.[121 Secondly,
significant phase segregation between PMN and PT occurred during the crystals
gro~th.[9-11,131 This results in the fluctuation of ~i~+-concentration in the grown PMN-PT
crystals, which in turn affects the piezoelectric properties of the single crystals. In order
to precisely and accurately control the chemical and thermal parameters for the PMN-PT
single crystal growth, it is necessary to know the melting point and the melting behaviour
of PMN-PT system. This has motivated us to study the high temperature phase diagram
of the PMN-PT system.
Although a lot of work has been undertaken on the crystal growth of (1-x)PMN-
xPT system, only a little attention has been paid to the study of the phase diagram. Ye et
al. previously reported the pseudo-binary PMN-PbO phase diagram determined by the
DTA method using the sealed platinum tubes.['" The melting point of PMN was found to
be T, = 1320 "C. In order to grow the single crystal of (1-x)PMN-xPT by the Bridgeman
technique, Luo et al. selected compositions with x = 0,0.30, 0.35, 0.40 mole fraction and
measured the melting points of these compositions by DTA (See Table 3.1).['] Based on
these melting points, a schematic phase diagram of (1-x)PMN-xPT solid solutions at high
temperature was sketched, from which the melting point of PbTiOs was read as 1256 "C.
However, this melting point is in discrepancy with the melting points T, = 1286 "C
reported by Moon et a1.[151 and 1295 "C by Fushimi et a ~ . " ~ ]
Table 3.1 Some melting points of (1-x)PMN-xPT solid solutions[91
x (mole fraction)
Melting point ("C)
0
1320
0.30
1296
0.35
1288
0.40
1284
1 .OO
1256
The purpose of this study is to establish a more detailed phase diagram of PMN-
PT solid solutions based on a systematic thermal analysis and to confirm the melting
point of PT.
3.1.1 Differential Thermal Analysis Measurements
Differential Thermal Analysis (DTA) was used in this work to determine the
phase transition (solid t, liquid) temperatures. A schematic set-up of DTA is illustrated
in Figure 3. I. ' '~]
+A\ Thermalcoup
Figure 3.1 Schematic set-up of differential thermal analysis
50
As shown in Figure 3.1, the DTA system has two sets of identical thermocouples
(platinum-platinum rhodium 13%). They are attached to the base of the sample and
reference holders, respectively, and connected 'back to back' (i.e. differentially). Two
positive sides (+) deliver a voltage V2, which indicates the temperature difference
between the sample and the reference. The reference temperature is monitored by V1.
Usually, a thermal stable material (A1203 powder in our case) is chosen as the reference.
When a thermal change occurs in the sample, whether it is endothermic or exothermic,
V2 will deviate from base line (zero) and form a peak, as shown in Figure 3.2. The
negative peak is called an endotherrn and the positive peak is called an exotherm. [I81
I V1 -- Reference Temperature (OC)
Figure 3.2 Typical endothermic and exothermic peaks of differential thermal
analysis.
The endotherm during melting has the following characteristic temperatures (See
also Figure 3.3).[19]
i) Extrapolated onset melting temperature (Ted -- The temperature corresponding to
the intersection (at B) of the tangent drawn at the point of the greatest slope in the
leading edge of the peak (BC) with the extrapolated base line (AB) when the melting
starts.
ii) Peak melting temperature (Tp& -- The temperature represented by the apex (at D) of
the melting peak.
iii) Extrapolated end melting temperature (Tfd -- The temperature corresponding to
the intersection (at F) of the tangent drawn at the point of the greatest slope in the
down-side leading edge of the peak (EF) with the extrapolated base line (FG) when
the melting finishes.
Likewise, the obtained exotherm during a solidifying process also has the similar
characteristic temperatures.
i) Extrapolated onset solidifying temperature (Tes)
ii) Peak solidifying temperature (Tp)
iii) Extrapolated end solidifying temperature (Tfs)
b Temperature ("C)
Figure 3.3 A typical endotherm showing the characteristic temperatures. Two
arrows indicate the heating direction.
Previous studies have shown that the extrapolated onset melting temperature
usually coincides with the phase transition equilibrium temperature during melting and is
less affected by the heating rate.[201
3.1.2 Constructing a Phase Diagram from Differential Thermal Analysis Curves
A phase diagram can be constructed from the information given by the DTA as
shown in Figure 3.4 for a continuous solid solution system.[211 In this figure, the vertical
solid curves represent the DTA heating curves at compositions with A, B, C and D. The
sharp peaks at the compositions of A and B indicate the phase transition (melting) of the
end substances, while the broad peaks at composition C and D indicate the melting of the
solid solutions (1-x)A-xB between A and B. The upper dashed line, connecting the
extrapolated end melting temperatures (Tfm), indicates the liquidus curve. The lower
dashed line, connecting the extrapolated onset melting temperatures (Tern), indicates the
solidus curve. Therefore, Tfm and Tern are also called the liquidus temperature and solidus
temperature, respectively.
T 2 em, A
T
Liquid
Solid solution
Liquidus
A Composition (X) B
em, B
Figure 3.4 A continuous solid solution phase diagram with superimposed
differential thermal analysis curves.
3.2 Experimental
3.2.1 Sample Preparation for Differential Thermal Analysis
To avoid the evaporation of PbO from PMN-PT samples during the differential
thermal analysis (DTA) measurements at high temperatures, PMN-PT powder sample
was sealed in a platinum (Pt) tube. The solid solutions of (1-x)PMN-xPT (0 5 x 5 1, at an
interval of 0.10 mole fraction) were prepared mainly following the detailed procedure
described in Section 2.2.1. The only change here is that the solid solutions were
synthesized at 950 OC for 8 hours instead of 900 "C for 4 hours (See Equation 3-1) to
increase the homogeneity of the solid solutions.
950•‹C, 8 hrs.
[(1-x)13]MgNb2O6 + PbO + xTiO2 - Pb(Mg113r\Tb213)1-xTix03 (3-1)
The powders were then ground for 1 hour, pressed into thin pellets, cut into small
pieces (-15 mg each), and loaded into a one-end sealed mini Pt tube (- 11.0 mm in
length, ID = 1.0 rnrn, OD = 2.0 mm). After that, the tube was heated on a hotplate at
about 400 OC for 1 hr to eliminate any moisture. The reason for this is that the moisture
would result in the leakage of the sealed Pt tube due to the water vapor pressure
established at high temperature. After heating, the open-end of the tube was quickly and
tightly clamped, and then hermetically sealed by propaneloxygen flame welding (See
Figure 3.5). During the welding process, the tube was held with two Pt plates for
dissipating heat.
Pt tube
Big steel plate for heat dissipation
Figure 3.5 Schematic sealing process for Pt tubes.
3.2.2 Thermogravimetry/Differential Thermal Analysis Measurements
The sealed tubes were tested by simultaneous thermogravimetry/differential
thermal analysis (TG/DTA) under static dry air at heating/cooling rates of 5 "Clmin
and/or 10 "C/min. Exstar TGIDTA 6300 (Seiko Instrument Inc.) was used for these
analyses. The resolution was 1 pV for DTA and 1 pg for TG. After each test, the tube
sample was examined with optical microscopy and analytical balance to check whether
TGIDTA is * 0.01 OC, the errors in determining the characteristic temperatures (T,, and
Tm, and Tes) are estimated to be k 2 OC
3.3 Results and Discussion
In order to study the high temperature behaviour of the PMN-PT solid solutions,
x-ray diffraction (XRD) and differential thermal analysis (DTA) were carried out on the
(1 -x)PMN-xPT solid solutions samples (x = 0.10 mole fraction internal).
3.3.1 X-ray Diffraction Spectra
Selected XRD spectra for (1-x)PMN-xPT (x = 0.30, 0.60, and 0.80) are illustrated
in Figure 3.6.
I Selected XRD patterns of (1-x)PMN-xPT solid solution 7
- Pyrochlore (1 1 0 ) ~ strongest peak -
T etragonal '""2: 0.20PMN-0.80PT J
29.3'
I , 0.40PMN-0.60PT Tetraganal
phase - -
Pigure 3.6 Selected x-ray diffraction spectra of (1-x)PMN-xPT solid solutions.
The pyrochlore phase is an undesirable phase in the synthesis of PMN-PT solid
solutions since it would deteriorate the ferroelectric properties.[221 The strongest peak of
the pyrochlore phase is at 29.3' on the 20 scale.[231 Figure 3.6 shows that no pyrochlore
phase has been detected in these samples within the detection limit of X-ray
diffractometer.
The indexed peaks in Figure 3.6 match the characteristic peaks of the perovskite
phase of the (1-x)PMN-xPT solid solutions,[241 indicating that these solid solutions have a
pure perovskite phase after synthesized at 950 OC.
Figure 3.6 also shows changes in the XRD spectra from 0.70PMN-0.30PT to
0.20PMN-0.80PT. 0.70PMN-0.30PT has a rhombohedral symmetry with lattice
parameters a = b = c (See Section 2.3.2.2). Therefore, the cubic (200) reflection for
0.70PMN-0.30PT has only one peak. On the other hand, 0.40PMN-0.60PT and
0.20PMN-0.80PT have a tetragonal structure (c > a = b) and therefore the cubic (200)
reflection has split into (200) and (002) peaks. Such a change of the cubic (200) peak
from 0.70PMN-0.30PT to 0.20PMN-0.80PT reflects the phase transformation from the
rhombohedral to the tetragonal phase with the increase of PT-content.
3.3.2 ThermogravimetryIDifferential Thermal Analysis
TGIDTA was performed on the samples of (1-x)PMN-xPT solid solutions. TG
profile of 0.40PMN-0.60PT is illustrated in Figure 3.7. It shows that no significant
weight loss could be detected within the detection limit of the instrument on the whole
heatinglcooling cycle. This confirms that the platinum mini-tube remained hermetically
sealed.
400 600 800 1000 1200 1400 Temperature ("C)
Figure 3.7 Thermogravimetry profile of 0.40PMN-0.60PT sample.
3.3.2.1 Effect of HeatingICooling Rate
The heatinglcooling rate in DTA measurements is important because it can affect
the peak shape and thus the characteristic temperatures. In order to find a suitable
heatingkooling rate for this system, DTA measurements are conducted at 10 OC/min
[Figure 3.8(a)], 5 "Clmin [Figure 3.8(b)], and 3 "Clmin [Figure 3.8(c)], respectively, on
the same sample of 0.10PMN-0.90PT. The extrapolated onset melting temperature (Tern),
the extrapolated end melting temperature (Tfm) and the extrapolated onset solidifying
temperature (T,,) derived from Figures 3.8 (a) - (c) are summarized in Table 3.2 (See
Section 3.1.1 for the definition of each of the above characteristic temperatures).
(a) 0.lOPMN-0.90PT Heating/ cooling at 10 OCImin
/ 1262
Cooling
Heating
Figure 3.8(a) (to be cont'ed)
(b) O.1OPMN-O.9OPT HeatingICooling at 5 OC/min -
1264
(Solidus temperature) (Liquidus temperature) -850 I I I I
1230 1250 1270 1290 1310
T ("0
-700
(c) 0.lOPMN-0.90PT Heating /Cooling at 3 O C/min
-800 I I I I
1230 1250 1270 1290 1310 T ("C)
Figure 3.8 Effect of heatinglcooling rates on the melting/solidifying temperatures for
0.10PMN-0.90PT (a) 10 "Clmin, (b) 5 OClmin, and (c) 3 OC/min.
Table 3.2 Effect of heating/cooling rate on the melting/solidifying temperatures of
O.1OPMN-0.90PT
Heating/
cooling rate
("Clmin)
Extrapolated onset melting temperature
Tern PC)
Extrapolated end melting temperature
Tfm ("C)
Width of endo-
thermic peak
(Tfm-Ted ("C)
Extrapolated onset
solidifying temperature
Tes ("0
The following observations [(a)-(c)] are drawn from Figure 3.8 and Table 3.2.
(a) Extrapolated onset melting temperature (Ted
The extrapolated onset melting temperatures (T,,) measured at the heating rates
of 10 "Clmin and 5 "Clmin are the same (1283 "C). This indicates that T,, is not affected
by these different heating rates, which is consistent with the general observation given in
Ref. [22]. However, the extrapolated onset melting temperature measured at 3 OCImin is
about 3 OC higher upon heating than those at 10 "Clmin and 5 "Clmin. This phenomenon
may be caused by experimental andlor DTA instrument error.
(b) Differences between extrapolated onset melting temperature (Tern) and
extrapolated onset solidifying temperature (Tes)
As the heatinglcooling rate decreases from 10 "Clmin to 3 "Clmin, the differences
between the extrapolated onset melting temperature (Tern) and the extrapolated onset
solidifying temperature (T,,), decrease from 18 "C to 11 "C. Under the true equilibrium
condition, Tcm and Tes should be This result confirms that the slower the
heatinglcooling rate is, the closer the system is to the equilibrium. However, in practice,
heatinglcooling at 3 "Clmin or less would shorten the lifetime of the heating elements of
DTA. Therefore, 5" Clmin heatinglcooling rate was chosen for the rest of the studies.
I
(c) Supercooling
It should be pointed out that even at the heating/cooling rate of 3 "Clmin, there is
still 11 "C difference between the onset melting temperature (Tern) and onset solidifying
temperature (Tes) [See Table 3.2 and Figure 3.8 (c)]. This thermal lag can be attributed to
supercooling.
Supercooling means the cooling of a liquid below its freezing (or solidifying)
temperature without the formation of the solid phase.[261 From the phase equilibrium
point of view, a melted liquid should be solidified when the temperature decreases to the
equilibrium crystallizing temperature. However, in reality, it is often possible to cool the
liquid below the true freezing (or solidifying) temperature before the crystallization
begins.
Supercooling is the result of the crystallization proceeding from nuclei. At the
equilibrium solidifying temperature, newly formed nuclei are very small and have high
surface energy. As a result, they are unstable and tend to disappear. Also at this
temperature, the critical nucleus size below which the spontaneous crystallization will not
64
occur, is very high. It is thus difficult for the newly formed nuclei to reach the critical
nucleus size. Therefore, the crystallization cannot happen at the equilibrium solidifying
temperature.
As the temperature falls, the critical nucleus size decreases rapidly.[271 Because of
the energy fluctuation, some nuclei reach the critical nucleus size and start to grow upon
the consumption of the other nuclei. The system energy becomes lower and the
solidification proceeds. As a result, supercooling is a necessary step for the crystals to
form and to grow.
Because of the supercooling, the solidifying temperature is usually lower than the
equilibrium transition temperature.r281 Therefore, in this study, the melting points were
obtained from the heating curves.
3.3.2.2 Differential Thermal Analysis Results of (1-x)PMN-xPT Solid Solutions
Figure 3.9 shows the DTA curve of 0.70PMN-0.30PT on a heatinglcooling run.
Upon heating, an endotherm appears between 1304 and 131 1 "C, indicating the melting
process of the compound. Upon cooling, an exothermic peak appears between 1296 and
1290 "C, corresponding to the solidifying process of the solid solution. According to the
definition in Sections 3.1.1, T,, = 1304 "C is the extrapolated onset melting temperature
(i.e. solidus temperature), and Tf, = 13 11 "C is the extrapolated end melting temperature
(i.e. liquidus temperature).
(Solidus temperature) (Liquidus temperature)
1230 1250 1270 1290 1310 1330 1350
T ("C)
Figure 3.9 Differential thermal analysis curves of 0.70PMN-0.30PT
In a DTA curve, the X-axis is a time axis and its conversion to a temperature scale
is dependent on the heatinglcooling rate.'"' Since the Y-axis of a DTA curve is a voltage
function, the integration of the curve (voltage versus time) will be proportional to the
energy that corresponds to the heat of fusion for melting. This relation can be described
by the equation (3-2) below.'Z11
Heat of fusion = K x A (3-2)
where K is the calibration constant, which can be obtained from the experiment by using
a known heat of fusion. A is the peak area, which could be measured accurately. Once
calibrated, the heat of fusion can be calculated from equation (3-2). Thus this method is
often used to quantitatively measure the heat of fusion of the melting. However, since the
latent heat of melting for the system studied in this work is not our primary concern, we
will not proceed further.
3.3.2.3 Determination of the Melting Point of PbTi03
As mentioned in Section 3.1, up to now, several melting points values of PbTi03
(PT) (e.g., 1256 "C, 1286 "C and 1295 "C) have been reported by different authors,
which are conflicting to each other. This is probably because different authors measured
it under different conditions. For example, some experiments were undertaken in an open
platinum pan without the tight control of the stoichiometry. We believe that an accurate
determination of the melting point of PT is essential for the construction of the PMN-PT
phase diagram.
In this study, the PT samples were prepared under the same condition as other
PMN-PT samples. The powder PT samples were sealed in a platinum tube. Therefore, the
evaporation of PbO was limited and the melting points determined by the DTA
measurement were more accurate.
Generally speaking, a melting transition would be truly isothermal only if the
material is theoretical 100% pure and the heatinglcooling rate is in equilibrium
condition.[191 In practice, a temperature range of melting process can usually be detected
in most "pure" substances by DTA measurements. In this study, PbTi03 was synthesized
through solid-state reactions and the homogeneity of PbTi03 cannot reach the atomic
scale. Moreover, the purity of starting chemicals (PbO + Ti02) is not 100%. Therefore, at
5 "Clmin heating rate, a temperature range of melting transition can clearly be detected as
shown in Figure 3.10. Upon heating, an endothermic peak appears between 1286 and
1293 "C, indicating the melting of PbTi03. The peak width is 7 "C. The same peak width
is also observed for the melting point of PMN single crystal measured in this study,
which shows a 7 "C difference between T,, and Tf,. It is generally accepted that the
melting point of most "pure" substances (or the end compounds in solid solution) should
be determined using the extrapolated onset melting temperature (T,,)'~]. From this
method, the melting point of PbTi03 is determined to be T,, = 1286 "C, which is in good
agreement with the melting temperature (1286 "C) obtained by Moon and ~ulrath,['~'
different from the data reported by Luo et a1 (1256 "c)'~] and by Fushimi et a1 (1295
0~).[161
Figure 3.10 also shows that the temperature difference between the extrapolated
onset melting temperature (T,, = 1286 "C) and the extrapolated onset solidifying
temperature (Tes = 1282 "C) is only 4 "C. This is much smaller than the difference of T,,
- T,, = 16 "C observed in the O.1PMN-0.9PT solid solution (See Table 3.2), indicating a
much weaker supercooling effect in the end compound PT than in the PMN-PT solid
solutions.
$ -1170 5. w Cooling 4
-1220 - 1286 L I E
I 1292
-1270 I I I I
1220 1240 1260 1280 1300
T ( O C )
Figure 3.10 Differential thermal analysis curves of PbTi03.
3.3.2.4 (1-x)PMN-xPT Solid Solution Phase Diagram
Based on the results obtained from the DTA, the melting points of (I-x)PMN-xPT
solid solutions (0 5 x 5 1) are summarized in Table 3.3.
Table 3.3 Summary of the melting points of the (1-x)PMN-xPT solid solutions
Extrapolated onset
x in mol%
Extrapolated end Melting
melting temperature
(Ted
melting temperature
(Tfd PC)
peak width
Tfm - Tern ("(3
All temperatures shown in Table 3.3 are obtained from the heating curves. T, is
the extrapolated onset melting temperature, and Th is the extrapolated end melting
temperature. (Th - T,,) is the width of the endothermic peak. In the case of x = 0, x =
70% and x = 100 %, that is PMN, 30PMN-70PT and PT, the extrapolated onset melting
temperature is considered as the melting points of these compositions as previously
discussed in the Section 3.3.2.3.
Based on the melting points in Table 3.3, a phase diagram of (1-x)PMN-xPT is
constructed in Figure 3.1 1.
Liquid (L)
0 PMN
Figure 3.11 High temperature phase diagram of the (1-x)PMN-xPT solid solutions
(From the DTA heating curves measured at 5 'Clmin).
In the phase diagram of Figure 3.11, for each composition, the extrapolated onset
melting temperatures (T,,) from the DTA curves are used as the solidus temperatures.
The extrapolated end melting temperatures (Tfm) are used as the liquidus temperatures.
The best fitting curve connecting all the solidus points forms the solidus line, and the best
fitting curve connecting all the liquidus points, forms the liquidus line. Thereby, the
phase diagram for the solid solution system has been constructed. In the phase diagram,
the solidus line and the liquidus line divide the phase diagram into three parts, the solid
solution region (SS), the liquid region (L) and the region with the coexistence of the solid
solutions (SS) and the liquid (L).
The phase diagram in Figure 3.11 shows that the solid solutions of Ph4N and PT
exhibits a minimum melting temperature (T,, = 1280 "C) at a composition of 70 mol% of
PbTi03. This temperature is lower than the melting points of PMN (T,, = 1323 "C) and
PT (T,, = 1286 "C). More data points should be obtained to verify the minimum melting
temperature.
The phase diagram in Figure 3.1 1 also illustrates that from 0 to 70 mol% PT, the
melting temperature for PMN-PT system decreases rapidly with the mol% PT, while
from 70 to 100 mol% PT, the melting temperature increases slightly with the mol% PT.
Moreover, the phase diagram indicates a two-phase region (liquid and solid
phases) around MPB (0.30 < x <0.39 mole fraction), which is an important composition
range for the growth of piezoelectric crystals. It can be seen that in an ideal equilibrium
crystallizing process, the solidified composition will be moved from S1 to S3 by internal
diffusion as temperature decreases from TI to T3. At T3, the overall solid composition
will come back to the original liquid composition (M, e.g. with 35% PT). However, in
real crystal growth, the diffusion proceeds very slowly. When the temperature decreases
from TI to T3, there will be a composition gradient between the first and last crystals.
This phenomenon is called phase segregation. The phase diagram shows that the
segregation will take place in the crystal growth of the MPB composition unless other
methods are adopted to reduce the phase segregation.
3.4 Conclusions
A high temperature phase diagram of (1-x)PMN-xPT solid solutions has been
established based on the DTA data obtained at the optimum of heatinglcooling rate of 5
"Clrnin. This phase diagram indicates a solid solution composition with a thermal
minimum (T,, = 1280 "C) at 70 mol% PT. The melting point of PT measured from this
experiment is 1286 "C. The phase diagram clearly indicates that the solidus temperature
and the liquidus temperature are different for the MPB compositions. Such a difference in
the solidus and liquidus temperatures is the origin of phase segregation in the MPB
crystals grown from the pure melt. This phase diagram provides quantitative information
on the possible composition occurred in the grown PMN-PT crystals and the phase
segregation.
3.5 References
[ l] Y. Yamashita, Y. Hosono, K. Harada, and N. Yasuda, IEEE Transactions on Ultrasonics, ferroelectrics, and frequency control, 49(2), 184 (2002).
[2] X.-W. Zhang and F. Fang, J. Mater. Res., 14(12), 4581 (1999).
[3] S-E. Park and T.R. Shrout, IEEE Transactions on Ultrasonics, Ferroelec trics, and Frequency Control, 44(5) 1140 (1997).
[4] S-E. Park and T.R. Shrout, Mater. Res. Innovations 1 ,20 (1997).
[5] K. Harada, S. Shimanuki, T. Kobayashi, S. Saitoh and Y. Yamashita, Key Eng. Mater. 157-158,95 (1999).
[6] T. Kobayashi, S, Shimanuki, S. Saitoh and Y. Yamashita, Jpn. J. Appl. Phys., Part 1 36,6035 (1997).
[7] R.S. Feigelson, Growth of large single crystals of relaxor ferroelectrics under controlled conditions, Piezoelectric Crystal Planning Workshop, Washington, DC, May 14-16 (1997).
[8] S.-G. Lee, R.G. Monteiro, R.S. Feigelson, H.S. Lee, M. Lee, S.-E. Park, Appl. Phys. Lett. 74, 1030 (1999).
[9] H. Luo, G. Xu, H. Xu, P. Wang and Z. Yin, Jpn. J. Appl. Phys. 39,5581 (2000).
[lo] G. Xu, H. Luo, P. Wang, H. Xu and Z. Yin, Chin. Sci. Bull. 45,491 (2000).
[ I l l G. Xu, H. Luo, H. Xu, Z. Qi, P. Wang, W. Zhong and Z. Yin, J. Crystal Growth 222, 202 (2001).
[12] M. Dong and Z.-G. Ye, J. Cryst. Growth, 209,81 (2000).
[13] R. S. Feigelson, Growth of PMNT and PZNT solid solution single crystal by the Bridgman Technique, DARPA sponsored PiezoCrystals Workshop, Washington, DC, Jan. 19-21 (2000).
[14] Z-G Ye, P. Tissot and H. Schmid, Mater. Res. Bull. 25,739 (1990).
[15] R. L. Moon and R. M. Fulrath, J. Amer. Ceram. Soc. 54, 124 (1971).
[16] S. Fushimi and T. Ikeda, J. Amer. Ceram. Soc. 50 129 (1967).
[17] A. R. West, Basic Solid State Chemistry, John wiley & Sons, Ltd, (Chichester, New York, Weinheim, Brisbane, Singapore, Toronto), England (1999), Chapter 4.
[18] M. E. Brown, Introduction to Thermal Analysis-Techniques and Application, Chapman and Hall, London and New York (1988), Chapter 4.
[19] J. L. Ford and P. Timmins, Pharmaceutical thermal analysis, Ellis Horwood Limited, Publishers Chichester, Halsted Press: a division of John Wiley & Sons, New York, Chichester, Brisbane, Toronto (1989), Chapter 2.
[20] G-W. Cui and Y. Huang, Phase Diagram and Phase Transition, Scientific Press, China (1978), Chapter 1 (in Chinese).
[21] P. J. Haines, Thermal Methods of Analysis, Blaclue academic & professional, An imprint of Chapman & Hall, London, Glasgow, Weinheim, New York, Tokyo, Melbourne, Madras (1995), Chapter 3.
[22] S. L Swartz and T. R. Shrout, Mater. Res. Bull. 17, 1245 (1982).
[23] JCPDS 25-443, PDF-2 Sets 1-43 database (1993).
[24] JCPDS 33-769, PDF-2 Sets 1-43 database (1993).
[25] R. P. Bauman, An Introduction to Equilibrium Thermodynamics, Prentice-Hall Inc., U.S.A (1966), Chapter 3.
[26] W. Hume-Rothery, J. W. Christian and W. B. Pearson, Metallurgical Equilibrium Diagrams, The Institute of Physics, London (1952), Chapter 10.
[27] G-W. Cui and Y. Huang, Phase Diagram and Phase transition, Scientific Press, China (1978), Chapter 6 (in Chinese)
[28] J. L. Ford and P. Timmins, Pharmaceutical Thermal Analysis, Ellis Horwood Limited, Publishers Chichester, Halsted Press: a division of John Wiley & Sons, New York, Chichester, Brisbane, Toronto (1989), Chapter 3.
Chapter 4 High Temperature Phase Diagram of
[0.65Pb(Mgl13NbU3)03-0.35PbTi03]-Pb0 System
4.1 Introduction
Relaxor ferroelectric (1-x)PMN-xPT (0 5 x 5 1 mole fraction) (designated as
PMN-PT) single crystals exhibit very high piezoelectric properties. Especially the single
crystals with the compositions close to the morphotropic phase boundary (MPB, x - 0.30
- 0.35 mole fraction)['], show a high dielectric constant (K = 5,000 - 6,000 at room
temperature), a very high piezoelectric coefficient (d33 > 2,000 pC/N), and a large
electromechanical coupling factor (k33 > 90%).[~-~' Such excellent performance makes
the PMN-PT single crystals the next generation electromechanical transducer materials
for a broad range of applications.
Recent studies on the crystal growth of the MPB composition
0.65Pb(Mgl,3Nbu3)03-0.35PbTi03 (designated as PMNT65135) shows that PMNT65135
is unstable above 1250 "C in the air and it partially decomposes into a pyrochlore
In order to prevent the decomposition at high temperature, flux should be used
as a solvent to grow the crystals at temperatures lower than that required for the growth
from the pure melt.
PbO has been an effective solvent for lead-containing perovskite ~ ~ s t e r n s . [ ~ - ~ ~ ' As
a solvent, PbO could help the formation of the perovskite phase during the crystallization
of the PMNT65135 system. The addition of 50 wt% PbO into PMNT65135 compound 76
also results in larger size perovskite crystals.r121 Besides, as a starting component of
PMN-PT solid solutions, PbO can avoid the contamination of foreign ions into the lattice
of the grown crystals. Therefore, PbO is usually used as a flux for PMNT65135 crystal
growth.
The work on the crystal growth of the (1-x)PMN-xPT system by the flux
technique ', 12-131 ha s shown that knowing the thermodynamic behaviour of the system
is very important. A reliable PMNT65135-Pb0 phase diagram will be very helpful for
choosing the optimum flux concentrations and temperature for the crystal growth.['31
Therefore, it is desirable to establish the high temperature phase diagram for the
PMNT65/35-Pb0 system.
So far, only a little attention has been paid on the study of the phase diagram of
PMNT-PbO system. Ye et al. first reported the PMN-PbO phase diagram determined by
the DTA method, which shows a eutectic melting behav io~r . [~~] The growth pathway
based on this phase diagram resulted in large and high quality PMN single crystals. More
recently, Dong and Ye published the pseudo-binary phase diagram of the
Pb(Znl~3Nbz3)o.91Tio.090~-Pb0 system by the DTA method.[14] The system shows a
eutectic behaviour at high temperatures. This phase diagram provides a useful guidance
for the growth of high quality and large PZNT crystals. These studies on the PMN-PbO
and PZNT-PbO systems provide some useful information (e.g., the eutectic behaviour)
for investigating the phase diagram of the PMNT65135-Pb0 system.
The purpose of this study is to establish the high temperature phase diagram of
PMNT65135-Pb0 system based on DTA measurements.
77
4.1.1 Characteristic Temperatures of an Endothermic Peak
An endothermic melting peak obtained from DTA measurements has the
following characteristic temperatures, as shown in Figure 4.1.''~~
i) Extrapolated onset melting temperature (Ted -- The temperature corresponding to
the intersection (at B) of the tangent drawn at the point of the greatest slope in the
leading edge of the peak, BC, with the extrapolated base line AB when the melting starts.
ii) Extrapolated end melting temperature (Tfd -- The temperature corresponding to
the intersection (at F) of the tangent drawn at the point of the greatest slope in the leading
edge of the peak, EF, with the extrapolated base line FG when the melting finishes.
Likewise, as a solidifying takes place upon cooling, the characteristic
temperatures for an exothermic peak are
i) Extrapolated onset solidifying temperature (Tes)
ii) Extrapolated end solidifying temperature (Tfs)
r
Temperature ("C)
Figure 4.1 Characteristic temperatures of an endothermic peak. Two arrows indicate
the heating direction
4.1.2 Constructing Eutectic Phase Diagram from Differential Thermal Analysis
A phase diagram with eutectic behaviour can be constructed from the information
given by DTA measurements, as shown in Figure 4.2. [ I6] In this figure, the vertical solid
lines represent the DTA heating curves at the compositions of A, B, C, D and E. The
sharp endothermic peaks at the end compositions of A and B indicate the melting of the
pure substances. The sharp endothermic peak at the composition of E illustrates the
melting of the eutectic composition. The two endothermic peaks at the compositions of C
and D show the effects of the eutectic melting and the continued melting until the
79
compounds are totally changed into liquid. The dashed curved lines, connecting both the
extrapolated onset melting temperature (T,,) of composition A, B, E, and the
extrapolated end melting temperatures (Tf,) of the liquidus peaks of compositions C and
D, are called the liquidus curves. The horizontal dashed straight line connecting the
extrapolated onset melting temperature (T,,) of the eutectic peaks for compositions C, D,
and E, indicates the eutectic (or solidus) line.
T em, A
T
TE
Liquid
Liquid + Solid A \
------ Solid
em Solidus
> \
T em, B
Composition (X) Figure 4.2 A eutectic phase diagram with superimposed differential thermal
analysis curves.
4.2 Experimental
In order to study the high temperature phase diagram of PMNT65135-Pb0 system,
XRD and Differential thermal analysis (DTA) were performed on a series of samples
with the composition (100-y)PMNT65/35-yPbO (0 5 y 5 100, at an interval of 10 weight
percent). Here weight percentage is used since it is a commonly used unit in the crystal
growth for convenience.
XRD was performed on the Philips powder diffractometer (Cu Ka, h = 1.5418
A). The angular resolution on the 20 scale for XRD was 0.05". The scan-step was set at
0.05" intervals. Thermal analysis was carried on simultaneous TGIDTA (Exstar TG/DTA
6300, Seiko Instrument Inc.). The resolution of the DTA is 1 pV.
PMNT65135 solid solution powders were prepared according to the procedure
described in Section 3.2.1. X-ray diffraction measurements were carried on the
PMNT6.5135 samples after the powders were synthesized at 950 "C for 8 hrs.
After the pure perovskite phase PMNT65135 powders were prepared, the powders
were mixed with PbO in different weight percentages, ground for 1 hr, pressed into thin
pellets, cut into small pieces, and loaded into a one-end-sealed mini Pt tube (OD = 2.0
mm, ID = 1.0 mm, -1 1.0 mm in length). After that, the tube was heated on a hot plate at
400 "C for 2 hrs to eliminate any moisture. Then, the open-end of the tube was quickly
and tightly clamped, and hermetically sealed by propaneloxygen flame welding. During
the welding process, the tube was held by two Pt plates for dissipating heat (see Figure
3.5 for the tube sealing).
The sealed Pt tubes were tested by DTA in static dry air at a heatinglcooling rate
of 5 "Clmin or 10 "Clrnin. After each test, the sample was examined by optical
microscopy and analytical balance to check whether there is any leakage on the sealed
tube. The temperature accuracy of TGIDTA is +. 0.01 "C, the errors in determining the
characteristic temperatures (Tern, Tfm and Tes) are estimated to be +- 2 "C.
4.3 Results and Discussion
4.3.1 X-ray Diffraction Spectra
XRD was performed on the PMNT65135 powder samples to check the phase
structure. As shown in Figure 4.3, XRD profile of PMNT65135 indicates that no
pyrochlore phase of Pb3Nb4013-type was detected within the detection limit of X-ray
diffractometer. Pb3Nb4013 is a thermodynamically more stable phase than the perovskite
phase, but functionally undesirable since it deteriorates the ferroelectric properties. The
indexed peaks in Figure 4.3 match the characteristic peaks of the perovskite phase of
~ ~ ~ ~ 6 5 1 3 5 . " ~ ~ These results show that the compound is pure perovskite phase.
Figure 4.3 X-ray diffraction pattern of 0.65PMN-0.35PT (PMNT65135) powder.
4.3.2 Differential Thermal Analysis
DTA was carried out on (100-y)PMNT65/35-yPbO (0 < y 5 100, at 10 wt%
interval) samples to study the melting and solidifying characteristics at high temperatures.
After each DTA test, no leakage was observed on the sealed tube under the optical
microscope and no weight loss was measured from the TG test (< f 1 pg). Selected tubes
were opened and examined under the optical microscope. Crystals instead of powders
were formed inside the sample tube, indicating that the powders experienced melting-
solidifying process during the DTA measurements.
4.3.2.1 Differential Thermal Analysis of PMNT65135
Figure 4.4 shows the effect of heatinglcooling rates (at 5 "Clmin and 10 OCIrnin)
on the meltinglsolidifying temperatures for pure PMNT65135 [i.e. y = 0 wt% for (100-
y)PMNT65/35-yPbO]. The melting and solidifying events were measured successively at
heatinglcooling rate of 5 "Clmin and then 10 "Clmin on the same sample.
The extrapolated onset melting temperature (T,,), the extrapolated end melting
temperature (Tf,) and the extrapolated onset solidifying temperature (Tes) derived from
Figure 4.4 are summarized in Table 4.1.
(a) PMNT65135 Heating/Cooling at 5 "Chin
1302 1309
I (b) PMNT65135
Figure 4.4 Differential thermal analysis curves of 0.65PMN - 0.35PT (PMN65/35) at
heatingfcooling rates of (a) 5 "C/min and (b) 10 "Clmin.
Table 4.1 Effect of heatinglcooling rates on the melting/solidifying temperatures for
PMNT65135
The following results [(a)-(c)] could be drawn from Figure 4.4 and Table 4.1.
Heating
cooling rate
("Clmin)
(a) Extrapolated onset melting temperature (Ted
At the heating rates of 10 "Clmin and 5 "Clmin, the extrapolated onset melting
temperatures (T,,) are the same (1302 "C), indicating that Tern is not affected by the
heating rates of the studied range. This result is consistent with the results obtained in
Section 3.3.2.1.
(b) Peak width (AT = Tfm-Ted
Extrapolated onset melting temperature
Tem OC)
With the heating rates increased from 5 "Clmin to 10 "Clmin, the width of the
endothermic peak (Tfm - T,,) increases from 7 "C to 11 "C. Since T,, was not affected by
the heating rate, this result shows that a faster heating rate results in a higher extrapolated
end melting temperature (Tfm).
Extrapolated end melting temperature Tfm PC)
Width of endo- therm
Tfm - Tern ("C)
Extrapolated onset
solidifying temperature
Tes W )
Tem - Tes ("(3
(c) Supercooling
Supercooling means the cooling of a liquid below its solidifying temperature
without the formation of the solid phase.['81 This phenomenon can also be observed on
PMNT65135 compound both at heatinglcooling rates of 10 "Clmin and 5 "Clmin by the
difference between the extrapolated onset melting temperature (T,,) and the extrapolated
onset solidifying temperature (T,,). As the heatinglcooling rate decreases from 10 "Clmin
to 5 "Clmin, the difference of T,, - TeS decreases from 37 to 8 "C (Figure 4.4 and Table
4.1). This result shows that a faster cooling rate could cause a more severe supercooling.
Therefore, the 5 "Clmin heatinglcooling rate was chosen for the rest of the work in this
experiment to reduce the supercooling.
Besides, upon cooling at 5 "Clmin rate [See Figure 4.4 (a)], in addition to the
exothermic peak of the solidification at 1294 "C, a small second exothermic peak appears
at 1286 "C, indicating another solidification event. This event may result from the partial
decomposition of the perovskite phase into the pyrochlore phase and PbO. Then, PbO
and PMNT form a binary system, which shows a solidus point at a temperature (1286 "C)
slightly lower than the solidification temperature of PMNT (1294 "C). The partial
decomposition was also found from the DTA results of Pb(Znl~3Nb213)o.91Ti0.0903 single
crystals.['41 However, the second exothermic peak is not observed at the heatinglcooling
rate of 10 "Clmin [Figure 4.4 (b)] since the severe supercooling, caused by a faster
cooling, may smear out any small event. Further studies should be done to verify the
composition of the second exothermic peak upon cooling on Figure 4.4 (a).
4.3.2.2 Differential Thermal Analysis of 6Owt % PMNT65135-40wt % PbO
Figure 4.5 presents the DTA curves of 60wt%PMNT65/35-40wt%PbO in the
temperature ranges of (a) from 750 to 1000 "C and (b) from 1000 to 1350 "C. The whole
DTA curve was plotted in two temperature ranges in order to see the small peaks. Upon
heating, two small endotherms appear. The first one at Tern = 850 "C (extrapolated onset
melting temperature) and the second one (very broad one) at Tfm = 1226 "C (extrapolated
end melting temperature) respectively [See Figure 4.5 (a) and (b)]. The first peak
indicates the start of the melting process and the second peak indicates the finish of the
melting process. Upon cooling, two exothermic peaks appear at 121 1 "C (sharp) and 827
"C (broad), respectively, corresponding to the start and finish of the solidification of the
60wt%PMNT65/35-40wt%PbO. The temperature difference between the endothermic
peak (T,, = 850 "C) and the exothermic peak (Tes = 827 "C) illustrates the supercooling at
a heatinglcooling rate of 5 "Clmin.
I (b) 1000 OC I T I 1350 OC
-500
Figure 4.5 Differential thermal analysis curve of 60wt%PMNT65/35-40wt%PbO.
Heatinglcooling rate of 5 "Clmin at temperature ranges:(a) 750 "C < T 5 1000 "C; (b)
1000•‹C S T < 1350•‹C.
-600
(a) 750 OC I T I 1000 OC -
827
-800 -
-900 I I 1 I
750 800 850 900 950 1000
T ("C)
4.3.2.3 Differential Thermal Analysis of 90wt%PMNT65/35-10wt%Pb0
Figure 4.6 shows the DTA curve of 90wt%PMNT65/35- 10wt%PbO. Upon
heating, a weak endothermic peak occurs at Tf, = 1300 "C. Upon cooling, a strong and
sharp exothermic peak appears at T,, = 1269 "C, indicating the solidification of the
compound. Compared with the DTA curve of 60wt%PMNT65/35-40wt%PbO (Figure
4 .3 , no peaks could be observed around 850 OC for 90wt%PMNT65/35-10wt%PbO [See
Figure 4.6 (a)]. This is because the composition of 90wt%PMNT65/35-10wt%PbO is
close to the PMNT65135 side, i.e. far away from the eutectic composition, and the peak
intensity around 850 OC is too weak to be detected.[lgl Further explanation will be given
in Table 4.3 and Figure 4.8.
(b) 1150 "C 5 T 5
-
Figure 4.6 Differential thermal analysis curves of 90wt%PMNT65/35-10wt%PbO in
the temperature ranges: (a) 750 "C I T I 1150 "C; (b) 1150 "C I T < 1350 "C.
4.3.2.4 Differential Thermal Analysis of 10wt%PMNT65/35-90wt%PbO
Figure 4.7 illustrates the DTA curves of 10wt%PMNT65/35-90wt%PbO. This
composition is closed to the PbO side. Upon heating, two consecutive peaks indicate two
endothermic events taking place at T,, = 840 "C and Tfm = 859 "C. Upon cooling, only
one broad exothermic peak occurred at Tfs = 839 "C. It is possible that the liquidus
solidification of the compound, which contained PbO in majority, was smeared out upon
cooling because the liquid PbO does not crystallize well.
I 10wt % PMNT65135-90wt % PbO
Figure 4.7 DTA curve of 10wt % PMNT65135-90wt % PbO.
92
4.3.3 Discussion on the Differential Thermal Analysis Results
Based on the data obtained from DTA, the melting points of the (100-y)wt%
PMNT65135-ywt%PbO system (0 I y I 100) are summarized in Table 4.2.
Table 4.2 Summary of the peak temperatures upon heating for (100-y)wt%
PMNT65135-ywt % PbO system
I O I Not detectable I 1302
y (wt% PbO)
1 l o I Not detectable I 1300
Eutectic temperature
TE (OC)
Liquidus Temperature
TL (OC)
50
60
70
80
90
843
853
1 100 I Not detectable
Not detectable
Not detectable
840
845
840
888[201
Not detectable
845
859
In Table 4.2, all peak temperatures shown were obtained from the heating curves
since the cooling temperature was affected by supercooling. TE represents the eutectic
temperature, obtained from the extrapolated onset melting temperature (T,,). TL is the
liquidus temperature, measured from the extrapolated end melting temperature (Tf,). The
following two observations can be made from Table 4.2.
(a) Eutectic temperature (TE) and liquidus temperature (TL)
Eutectic temperature TE is found to be averaged at 846 "C excluding y = 0, 10,
100 wt% of PbO, where the eutectic peaks were not detectable. Table 4.2 shows that the
liquidus temperatures TL decrease from 1302 "C (0 %wt PbO) to 1226 "C (40 wt% PbO)
and increases from 845 "C (80 wt% PbO) to 888 "C (100 wt% PbO). The results indicate
that PMNT65135-Pb0 exhibits eutectic behaviour at high temperature.
(b) Explanation of the non-detectable peaks
The eutectic temperatures were not detectable for the composition with y = 10
wt% PbO. When the composition is close to the eutectic, the intensity of the eutectic peak
becomes higher. At the eutectic composition, the intensity of the peak reaches the
maximum. 1214] AS the composition y = 10 wt% PbO is far away from the eutectic
composition, the eutectic peak becomes too weak to be detected.
Table 4.2 also shows that the liquidus temperatures (TL) were not detectable at y =
50, 60 and 70 wt% PbO. As the composition is moving relatively far away from
PMNT65135, the liquidus peak intensity decreases, and the peak becomes too weak to be
detected for compositions with ypbo = 50, 60 and 70 wt%. In our experiments, the DTA
signals of the samples were particularly weak because of the relative small mass of the
sample (- 15 mg) compared with the mass of Pt tube (-550 mg), which makes the weak
thermal events difficult to be detected.
Table 4.2 shows that at high temperatures, the (100-y)wt%PMNT65/35-ywt%PbO
system forms a pseudo-binary system with eutectic behaviour. "Pseudo" is used since
PMNT65135 is a solid solution itself rather than a simple compound.
In order to determine the eutectic composition of the system, a "maximized peak
area method" was used.[191 This method is based on the principle that the area under the
DTA peak for the eutectic melting achieves the maximum at the eutectic concentration.
The normalized (by sample weight) peak areas around the eutectic composition are
summarized in Table 4.3 and plotted in Figure 4.8.
Table 4.3 Summary of the eutectic peak area obtained from differential thermal
analysis for the PMNT65135-Pb0 system
PbO in weight percent (%)
Normalized peak area ** (pV x seclmg)
* The peak area for 100% PbO at eutectic temperature was deduced as 0 pV x seclmg.
** Normalized by the powder sample weight.
Figure 4.8 Determination of the eutectic composition from differential thermal
analysis for the (100-y)PMNT65/35-yPbO system.
Figure 4.8 shows that the DTA eutectic peak area increases as the composition
increases from 40 to 80 wt% of PbO. At y = 80 wt% PbO, the peak area reaches
maximum. Then, from 80 to 100 wt% of PbO, the peak area decreases. Therefore, the
eutectic composition is located at y~ = 80 wt% PbO (at an interval of 10 wt% PbO).
4.3.4 PMNT65135 - PbO Pseudo-Binary Phase Diagram
Based on the information obtained in Section 4.3.3, a pseudo-binary phase
diagram of the (100-y)wt%PMNT65/35-ywt%PbO system (0 < y < 100) is constructed as
shown in Figure 4.9.
Liquidus
Eutectic TE = 846 + 7 OC
Liquid
\ \ , Liquidus 1
PMNT65135 (s) + PbO (s) yE = 80 wt% PbO
700 I I I I I I I I I
40 50 60 70 80 90 100 y (wt%PbO) PbO
Figure 4.9 Phase diagram of the (1-y)PMNT65/35-yPb0 system.
In Figure 4.9, TE = 846 O C represents the eutectic temperature and was determined
from the average of the eutectic temperatures at y = 20,30,40,50,60,70, 80 and 90%wt
PbO (See Table 4.2). Dashed line shows the extrapolated liquidus temperature curve for
50, 60 and 70 wt% PbO, where the liquidus peak could not be detected from our DTA
measurements. Dash dot lines indicate the extrapolated eutectic temperatures for 0, 10
and 100wt% PbO.
Figure 4.9 illustrates that the PMNT65135-pb0 binary system exhibits eutectic
behaviour at high temperatures. The eutectic composition is located at 80wt% PbO, and
the eutectic temperature (TE) is around 846 "C. It can be seen that the melting point of
PMNT65135 (1302 "C) or PbO (888 "C) is depressed by adding PbO to PMNT65135 or
PMNT65135 to PbO. The maximum depression of the melting points (846 "C) occurs at
the eutectic composition (YE " 80 wt% PbO).
4.4 Conclusions
In conclusion, a high temperature phase diagram of the pseudo-binary (100-
y)wt% PMNT65135-ywt%PbO system has been established based on the DTA
measurements. The phase diagram shows that the pseudo-binary system exhibits a
eutectic melting behaviour with the eutectic composition at 20wt%PMNT65/35-
80wt%PbO. The eutectic temperature was determined at 846 "C. The established phase
diagram of the (100-y)wt%PMNT65/35-ywt%PbO system has defined the eutectic point
and the liquidus curves. It provides thermodynamic information on the melting and
solidifying of the system, which is useful for the growth of large and high quality
PMNT65135 crystal by the flux, the solution Bridgman and other techniques.
4.5 References
[I] T. R. Shrout, Z. P. Chang, N. Kim and S. Markgraf, Ferroelectr. Lett. 12,63 (1990).
[2] X.-W. Zhang and F. Fang, J. Mater. Res. 14(12), 4581 (1999).
[3] S-E. Park and T.R. Shrout, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 44(5), 1140 (1997).
[4] S-E. Park and T.R. Shrout, Mater. Res. Innovations 1,20 (1997).
[5] K. Harada, S. Shimanuki, T. Kobayashi, S. Saitoh and Y. Yarnashita, Key Eng.
Mater. 157-158,95 (1999).
[6] T. Kobayashi, S. Shimanuki, S. Saitoh and Y. Yamashita, Jpn. J. Appl. Phys., Part 1 36,6035 (1997).
[7] 2.-G. Ye, M. Dong, and Y. Yamashita, J. Cryst. Growth 211,247 (2000).
[8] H.-S. Luo, G.-Sh. Xu, H. Xu, P.-Ch. Wang and Zh.-W. Yin, Jpn. J. Appl. Phys. 39, 558 1 (2000).
[9] Y. Yamashita and S. Shimanuki, Mater. Res. Bull. 31, 887 (1996).
[lo] Z.-G. Ye, P. Tissot and H. Schmid, Mater. Res. Bull. 25,739 (1990).
[ l l ] L. Zhang, Master's Thesis, Simon Fraser University, Chapter 3, (2000).
[12] Z.-G. Ye and H. Schmid, J. Cryst. Growth 167,628 (1996).
[13] M. Dong and Z.-G. Ye, J. Cryst. Growth 209, 81 (2000).
[14] M. Dong and Z.-G. Ye, Jpn. J. Appl. Phys. 40 4604 (2001).
[15] J. L. Ford and P. Timmins, Pharmaceutical Thermal Analysis, Ellis Horwood Limited, Publishers Chichester, Halsted Press: a division of John Wiley & Sons, New York, Chichester, Brisbane, Toronto (1989), Chapter 2.
[16] P. J. Haines, Thermal Methods of Analysis, Blackie Academic & Professional, An imprint of Chapman & Hall, London, Glasgow, Weinheim, New York, Tokyo, Melbourne, Madras (1995), Chapter 3.
[17] JCPDS 33-769, PDF-2 Sets 1-43 database, 1993.
[18] W. Hume-Rothery, J. W. Christian and W. B. Pearson, Metallurgical Equilibrium Diagrams, The Institute of Physics, London (1952), Chapter 10.
[I91 M. E. Brown, Introduction to Thermal Analysis-Techniques and Application, Chapman and Hall, London and New York (1988), Chapter 4.
[20] S. Fushimi and T. Ikeda, J. Amer. Ceram. Soc. 50(3) (1967)
Chapter 5 Summary
A new phase diagram for the (1-x)PMN-xPT solid solutions in the vicinity of the
MPB has been established, in which the stability region of the monoclinic phase is found
to be 0.31 5 x 5 0.37 mole fraction at temperature range 20 K. This composition range
narrows at 300 K. From 20 to 500 K, the monoclinic phase changes to the tetragonal
phase then to the cubic phase. The existence of a secondary phase in this range, either
tetragonal or rhombohedra1 phase, has been observed in all the MPB compositions.
Lattice parameters are also calculated based on the synchrotron XRD for 0.305 x 5 0.39.
This phase diagram, published in Phys. Rev. B. (2002), provides valuable information for
understanding the nature of the MPB.
A high temperature phase diagram of (1-x)PMN-xPT solid solutions has been
constructed based on the DTA data obtained at the heatinglcooling rate of 5 "Clmin. This
phase diagram has a solid solution form with a thermal minimum (T,, = 1280 "C) at 70
mol%PT. The melting point of PT measured from this experiment is 1286 "C. The phase
diagram indicates that the solidus temperature and the liquidus temperature are different
for MPB composition. Since the difference in the solidus and liquidus temperature is the
origin of phase segregation in crystal growth, this phase diagram provides quantitative
information on the possible composition occurred in the grown PMN-PT crystals and the
phase segregation rate. This information will allow the crystal growers to develop and
improve growth techniques to minimize the phase segregation and to maximize the PMN-
PT crystal homogeneity.
A high temperature phase diagram of the pseudo-binary (100-y)wt%
PMNT65135-ywt%PbO system has been established based on the DTA measurements.
The phase diagram shows that (100-y)wt%PMNT65/35-ywt%PbO exhibits a eutectic
melting behaviour with the eutectic composition of 20wt%PMNT65/35-80wt%PbO. The
eutectic temperature was determined to be 846 +- 7 "C. The established phase diagram has
defined the eutectic point and the liquidus curves of the pseudo-binary system. It provides
thermodynamic information on the melting and solidifying of the system, which is useful
for the growth of large and high quality PMNT65135 crystal by the flux technique.
Appendix Pseudo-Voigt Function
A pseudo-Voigt function is defined as the convolution of Lorenztian and Gaussian
functions as shown in Equation (A-1)'":
Voigt ,,,, = (1 - q) Gauss (x, T) + q Lorenz (x, r ) (A-1)
where, x is related to the diffraction angle 28. q is the mixing parameter and represents
the weight fraction of each function (Gauss function and Lorenz function) in the pseudo-
Voigt function. q is computed as Equation (A-2)
rL in Equation (A-2) is the full width at half maximum of Lorentzian function. r
is the peak width (full width at half maximum, FWHM) and is computed as Equation (A-
3):
where rG is the full width at half maximum of Gaussian function
Gaussian function is defined in Equation (A-4)
2 J l n 2 Gauss (x, r) = &
Lorenztian function is defined in Equation (A-5)
2 Lorenz (x, r)= -
?f'L
Reference:
[I] P. Thompson, D. E. Cox and I. B. Hastings, J. Appl. Cryst. 20,79 (1987).
