Zuo-Guang. Ye Advanced Dielectric Piezoelectric and Ferroelectric Materials: Synthesis, Characterisation and Applications
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Handbook of dielectric, piezoelectric and ferroelectric materials170
6.4 Conclusions and future trends
The SSCG method has been applied to the growth of high-performance
piezoelectric single crystals such as Ba(Zr,Ti)O
3
, PMN–PT, and PMN–PZT.
In the case of Ba(Zr,Ti)O
3
solid solution, the single crystals grew up to
50 mm in lateral dimension. Rhombohedral Ba(Zr
0.075
Ti
0.925
)O
3
single crystals
exhibit a k
33
of about 0.9 and a d
33
of about 1000 pC/N at room temperature
and are thus promising candidates for high-performance and lead-free
piezoelectrics. The undoped, Fe-doped, and Mn-doped 70PMN–30PT single
crystals were produced by SSCG. The doping does not make their single
crystal growth process more complicated and thus chemically uniform doped
PMN–PT single crystals were successfully grown by the SSCG process. The
PMN–PZT single crystals with different ratios of PMN/PZ/PT as well as
different T
RT
were fabricated by SSCG. By changing the ratios of PMN/PZ/
PT in the PMN–PZ–PT system, the dielectric and piezoelectric properties of
PMN–PZT single crystals could be easily controlled.
It was demonstrated in this chapter that the SSCG method is a very
effective way of producing high-performance piezoelectric single crystals
such as BaTiO
3
, Ba(Ti,Zr)O
3
, PMN–PT, and PMN–PT–PZ. Up to now, the
SSCG technique has been the only way for growth of large relaxor–PZT
single crystals. Therefore, the SSCG process will provide a breakthrough in
the fabrication of high-performance piezoelectric single crystals, especially
the high T
C
relaxor–PZT single crystals.
6.5 References
1. S. E. Park, T. R. Shrout, ‘Ultrahigh strain and piezoelectric behavior in relaxor based
ferroelectric single crystal,’ Journal of Applied Physics 82 (4) 1804–1811 (1997).
2. S. E. Park, T. R. Shrout, ‘Characteristics of relaxor-based piezoelectric single crystals
for ultrasonic transducer,’ IEEE Trans on Ultrasonics, Ferroelectrics, and Frequency
Control Special Issues on Ultrasonic Transducer 44 (5) 1140–1146 (1997).
Table 6.3
Dielectric and piezoelectric properties of PMN–PZT single crystals grown
by the SSCG process
(001) (001) (001) (001) (001)
PMN–PZT-1 PMN–PZT-2 PMN–PZT-3 PMN–PZT-4 PMN–PZT-5
K
3
T
6000 5000 4200 3500 3000
tan δ > 0.01 > 0.01 > 0.01 > 0.01 > 0.01
T
C
[°C] 200 200 195 190 190
T
RT
[°C] 100 115 130 145 160
k
33
0.92 0.92 0.9 0.9 0.89
d
33
[pC/N] 2000 1750 1450 1250 1000
d
32
(011)/ pC/N] 1900 1700 1400 1100 850
<100>
WPNL2204
Development of high-performance piezoelectric single crystals 171
3. P. W. Rehrig, S. E. Park, S. Trolier-McKinstry, G. L. Messing, B. Jones, T. R. Shrout,
‘Piezoelectric properties of zirconium-doped barium titanate single crystals
grown by templated grain growth,’ Journal of Applied Physics 86 (3) 1657–1661
(1999).
4. T. R. Shrout, Z. P. Chang, N. Kim, S. Markgraf, ‘Dielectric behavior of single crystal
near the (1–x)Pb(Mg
1/3
Nb
2/3
)O
3
–(x)PbTiO
3
morphotropic phase boundary,’
Ferroelectrics Letters 12 63–69 (1990).
5. M. Dong, Z. G. Ye, ‘High-temperature solution growth and characterization of the
piezo-/ferroelectric (1–x)Pb(Mg
1/3
Nb
2/3
)O
3
–xPbTiO
3
[PMNT] single crystals,’ Journal
of Crystal Growth 209 81–90 (2000).
6. X. Jiang, F. Tang, J. T. Wang, T. P. Chen, ‘Growth and properties of PMN-PT single
crystals,’ Physica C 364–365 678–683 (2001).
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, ‘Growth
and electrostrictive properties of Pb(Mg
1/3
Nb
2/3
)O
3
crystals,’ Applied Physics Letters
74 (7) 1030–1032 (1999).
9. G. Xu, H. Luo, H. Xu, Z. Qi, P. Wang, W. Zhong, Z. Yin, ‘Structural defects of
Pb(Mg
1/3
Nb
2/3
)O
3
–PbTiO
3
single crystals grown by a Bridgman method,’ Journal of
Crystal Growth 222 202–208 (2001).
10. K. T. Zawilski, M. C. C. Custodio, R. C. DeMattei, S. G. Lee, R. G. Monteiro, H.
Odagawa, R. F. Feigelson, ‘Segregation during the vertical Bridgman growth of lead
magnesium niobate–lead titanate single crystals,’ Journal of Crystal Growth 258
353–367 (2003).
11. T. M. Heo, J. B. Lee, D. H. Kim, H. Y. Lee, N. M. Hwang, J. K. Park, U. J. Chung,
D. Y. Kim, ‘Solid-state single crystal growth of BaTiO
3
and PMN-PT,’ in Morphotropic
Phase Boundary Perovskites, High Strain Piezoelectrics, and Dielectric Ceramics,
Ceramic Transactions, Wiley, Indianapolis 136 211–218 (2003).
12. H.-Y. Lee, ‘Solid state single crystal growth (SSCG) method: a cost-effective way of
growing piezoelectric single crystals,’ pp. 160–177 in Piezoelectric Single Crystals
and Their Application, Edited by S. Trolier McKinstry, Y. Yamashita and L. E. Cross
Penn State University, State College, (2004).
13. S. Matsuzawa, S. Mase, ‘Method for producing a single crystal ferrite,’ US Patent
No. 4339301 (1982).
14. K. Kugimiya, K. Hirota, K. Matsuyama, ‘Process for producing single crystal ceramics,’
US Patent No. 4900393 (1990).
15. T. Yamamoto, T. Sakuma, ‘Fabrication of barium titanate single crystals by solid-
state grain growth,’ Journal of the American Ceramic Society 77 (4) 1107–1109
(1994).
16. Y. S. Yoo, M. K. Kang, J. H. Han, H. Kim, D. Y. Kim, ‘Fabrication of BaTiO
3
single
crystals by using exaggerated grain growth method,’ Journal of the European Ceramic
Society 17 1725–1727 (1997).
17. P. W. Rehrig, G. L. Messing, S. Trolier-McKinstry, ‘Templated grain growth of
barium titanate single crystals,’ Journal of the American Ceramic Society 83 (11)
2654–2660 (2000).
18. H. Y. Lee, J. S. Kim, D. Y. Kim, ‘Fabrication of BaTiO
3
single crystals using
secondary abnormal grain growth,’ Journal of the European Ceramic Society 20
1595–1597 (2000).
WPNL2204
Handbook of dielectric, piezoelectric and ferroelectric materials172
19. T. Li, A. M. Scotch, H. M. Chan, M. P. Harmer, ‘Single crystals of
Pb(Mg
1/3
Nb
2/3
)O
3
–35 mol% PbTiO
3
from polycrystalline precursors,’ Journal of the
American Ceramic Society 81 (1) 244–248 (1998).
20. A. Khan, F. A. Meschke, T. Li, A. M. Scotch, H. M. Chan, M. P. Harmer, ‘Growth
of Pb(Mg
1/3
Nb
2/3
)O
3
–35 mol% PbTiO
3
single crystals from (111) substrates by seeded
polycrystal conversion,’ Journal of the American Ceramic Society 82 (11) 2958–
2962 (1999).
21. B. Jaffe, W. R. Cook, H. Jaffe, Piezoelectric Ceramics, Academic Press, London and
New York (1971).
22. Y. H. Bing, Z. G. Ye, ‘Synthesis, phase segregation and properties of piezo-/ferroelectric
(1–x)Pb(Sc
1/2
Nb
1/2
)O
3
–xPbTiO
3
single crystals,’ Journal of Crystal Growth 287 326–
329 (2006).
23. S. Zhang, P. W. Rehrig, C. Randall, T. R. Shrout, ‘Crystal growth and electrical
properties of Pb(Yb
1/2
Nb
1/2
)O
3
–PbTiO
3
perovskite single crystals,’ Journal of Crystal
Growth 234 415–420 (2002).
24. N. Yasuda, H. Ohwa, M. Kume, K. Hayashi, Y. Hosono, Y. Yamashita, ‘Crystal
growth and electrical properties of lead indium niobate–lead titanate binary single
crystal,’ Journal of Crystal Growth 229 299–304 (2001).
25. S. Zhang, L. Lebrun, S. Rhee, R. E. Eitel, C. A. Randall, T. R. Shrout, ‘Crystal
growth and characterization of new high Curie temperature (1–x)BiScO
3
–xPbTiO
3
single crystals,’ Journal of Crystal Growth 236 210–216 (2002).
26. Y. Hosono, Y. Yamashita, H. Sakamoto, N. Ichinose, ‘Large piezoelectric constant of
high-Curie-temperature Pb(In
1/2
Nb
1/2
)O
3
–Pb(Mg
1/3
Nb
2/3
)O
3
–PbTiO
3
ternary single
crystal near morphotrophic phase boundary,’ Japanese Journal of Applied Physics
41 (11A) L1240–L1242 (2002).
27. Y. Hosono, Y. Yamashita, H. Sakamoto, N. Ichinose, ‘Dielectric and piezoelectric
properties of Pb(In
1/2
Nb
1/2
)O
3
–Pb(Mg
1/3
Nb
2/3
)O
3
–PbTiO
3
ternary ceramic materials
near the morphotrophic phase boundary,’ Japanese Journal of Applied Physics 42
(2A) 535–538 (2003).
WPNL2204
173
7.1 Introduction
Single crystals of the solid solutions between the relaxor ferroelectrics
Pb(Mg
1/3
Nb
2/3
)O
3
(PMN) and Pb(Zn
1/3
Nb
2/3
)O
3
(PZN), and the normal
ferroelectric PbTiO
3
(PT), namely, PMN–PT and PZN–PT, have attracted a
great deal of attention over the past years because of their high dielectric
constant and extraordinary piezoelectric properties, with a strain levels
exceeding 1% and an electromechanical coupling factor k
33
> 90% (Park and
Shrout, 1997; Kuwata et al., 1981), which outperform the state-of-the-art
PZT-based piezoceramics (with 0.1% and 70–75%, respectively). The
electromechanical performance of these crystals makes them the materials
of choice for the next generation of acoustic transducers.
An intense program of materials development and device demonstrations
has been undertaken under the sponsorships of the US Defense Advanced
Research Projects Agency and the Office of Naval Research, which has
advanced the materials technology to the level of prototype quantities/costs
and confirmed the considerable potential – enhanced device sensitivity, source
level, bandwidth and compactness – originally envisioned for Navy SONAR
devices (Cross, 2004; Park and Shrout, 2002; Yamashita et al., 2002). On the
other hand, a wide range of advanced applications based on these innovative
piezocrystals is also being actively pursued in the civilian sectors, including
medical ultrasonic diagnostics and therapy, active machine tool control and
vibration suppression (see Chapters 3 and 4). For example, the excellent
properties of the piezocrystals used in the medical ultrasonic imaging system
have resulted in dramatic improvements in the efficiency, sensitivity and
bandwidth of the ultrasound transducers (Philips, 2004; Chen and Panda
2004).
However, there are several issues regarding future applications of the
PMN–PT and PZN–PT crystals. One of them is a low Curie temperature
(T
C
< 160 °C) and especially an even lower depoling temperature (T
MPB
<
100 °C) in these crystals because of the presence of a morphotropic phase
7
Piezo- and ferroelectric
(1–
x
)Pb(Sc
1/2
Nb
1/2
)O
3
–
x
PbTiO
3
solid solution system
Y-H BING and Z-G YE,
Simon Fraser University, Canada
WPNL2204
Handbook of dielectric, piezoelectric and ferroelectric materials174
boundary (MPB). The low T
MPB
and T
C
cause the materials to be depoled
easily, reduce the thermal stability of dielectric and piezoelectric properties,
limit the acoustic power and the temperature range of operation of the devices
and also make the device fabrication processing more difficult (Park and
Shrout, 2002; Yamashita et al., 2002). These drawbacks would significantly
reduce the piezoelectric response and thereby diminish the performance of
the transducer devices. Therefore, high temperature stability is necessary for
applications in many areas.
To solve these issues, active studies have been pursued on several compounds
with higher T
C
. Piezoelectric single crystals of (1–x)Pb(Yb
1/2
Nb
1/2
)O
3
–xPbTiO
3
solid solution were grown using a flux technique and the electromechanical
properties were reported by Zhang et al. (2002a,b). The Curie temperature of
the grown crystals lies in the range of 300–400 °C. The piezoelectric coefficient
d
33
is high and reaches approximately 2500 pC/N for the <001>-oriented
PYN–46%PT single crystals. The system of (1–x)BiScO
3
–xPbTiO
3
with
MPB compositions was synthesized in the form of ceramics with a Curie
temperature of 430 °C and a d
33
of 450 pC/N at a composition of x = 0.64
(Eitel et al., 2001). The (1–x)BiScO
3
–xPbTiO
3
single crystals were grown
using a flux method. The Curie temperature of rhombohedral crystals was
found to be about 404 °C, with a rhombohedral–tetragonal phase transition
temperature around 350 °C (Zhang et al., 2003). Single crystals of
(1–x)Pb(In
1/2
Nb
1/2
)O
3
–xPbTiO
3
and their electromechanical properties were
also reported with a T
C
around 320 °C and a d
33
of 400 pC/N (Yasuda et al.,
1999, 2000a,b).
Despite the above encouraging results, continued research on other new
MPB systems of high T
C
piezoelectric materials in the form of ceramics and
single crystals constitutes an important area of investigation for the future
development of high-temperature transducers operating at temperatures much
higher than room temperature. The solid solution of (1–x)Pb(Sc
1/2
Nb
1/2
)O
3
–
xPbTiO
3
has emerged as an interesting system to study and exploit because
it shows the existence of an MPB with a Curie temperature T
C
> 200 °C.
The solid solution of (1–x)Pb(Sc
1/2
Nb
1/2
)O
3
–xPbTiO
3
[(1–x)PSN–xPT])
is formed between the relaxor Pb(Sc
1/2
Nb
1/2
)O
3
and the normal ferroelectric
PbTiO
3
. Pb(Sc
1/2
Nb
1/2
)O
3
(PSN) was first synthesized in the form of ceramics
by Smolenskii et al. (1959). This compound has the perovskite structure and
its Curie temperature is T
C
= 90 °C. Single crystals of PSN were grown using
the flux method with PbO or PbO–B
2
O
3
as flux (Yanagisawa et al., 1998).
The study of the (1–x)PSN–xPT binary system was first reported by Tennery
et al. (1968) based on the experiments on ceramic specimens. Very high
peak values (about 26 000) of dielectric constant, with the peak value of loss
in the order of 0.05 to 0.08, were observed at x = 0.20. The rhombohedral
symmetry was assigned for the composition x < 0.425 and tetragonal for x >
0.45 at room temperature. In the range of 0.425 ≤ x ≤ 0.45, a mixture of
WPNL2204
Piezo- and ferroelectric (1–
x
)Pb(Sc
1/2
Nb
1/2
)O
3
–
x
PbTiO
3
175
rhombohedral and tetragonal phases was proposed. The piezoelectric radial
coupling coefficient (k
p
) was studied as a function of x and the maximum
value of k
p
= 0.46 was observed with x = 0.425, which falls into the region
of two-phase coexistence. A preliminary phase diagram was established by
means of dielectric measurements and a two-phase region corresponding to
the composition around x = 0.425 with a Curie temperature around 260 °C
was roughly sketched (Fig. 7.1).
After Tennery’s work, only few studies were carried out on the (1–x)PSN–
xPT compounds. Yamashita (1994a) reported the large electromechanical
coupling factors of k
p
= 71%, k
33
= 77%, and a piezoelectric coefficient d
33
= 450 pC/N for the (1–x)PSN–xPT ceramics and the Nb-doped (1–x)PSN–
xPT ceramics with x = 0.43. Later, Yamashita et al. (1996, 1997) reported the
crystal growth and electrical properties of the (1–x)PSN–xPT single crystals
grown by a flux method using PbO–B
2
O
3
as the solvent. The chemical
analysis revealed that the composition of the crystals is in the range of 0.33
to 0.35, which is different from the initially weighed MPB composition of
x = 0.42. The <001>-oriented crystal showed a dielectric constant peak of
60 000 at the T
C
of 206 °C, a remnant polarization P
r
= 26
µ
C/cm
2
, a coercive
field E
C
= 6 kV/cm and a coupling factor k
33
= 72%.
Nevertheless, there are several issues concerning the growth of (1–x)PSN–
xPT crystals that have not been resolved. Because of the very high melting
point, T
m
> 1425 °C (Yanagisawa et al., 1998) of the solid solution system,
difficulties were encountered in the growth. Consequently, the dielectric and
piezoelectric properties of the (1–x)PSN–xPT crystals have not been fully
Composition parameter
x
PSN PT
1.000.800.600.400.200.00
600
500
400
300
200
100
0
Temperature (°C)
Two phase
Rhombohedral
Tetragonal
Cubic
7.1
Original temperature vs. composition phase diagram for the (1–
x
)Pb(Sc
1/2
Nb
1/2
)O
3
−
x
PbTiO
3
system (after Tennery
et al.
, 1968).
WPNL2204
Handbook of dielectric, piezoelectric and ferroelectric materials176
studied and exploited owing to the poor quality and the significant composition
fluctuations of the crystals grown previously.
On the other hand, there are several fundamental issues regarding the
(1–x)PSN–xPT system in general that remain to be understood. First, the
MPB region of the solid solution is not yet clearly defined. The preliminary
phase diagram in Fig. 7.1 only sketched the region of two-phase coexistence,
lacking detailed information on phase symmetry and phase components. A
more complex MPB was found in the PZT system (Jaffe et al., 1971; Noheda
et al., 1999), and then in the PZN–PT (Kuwata et al., 1981; La-Orauttapong
et al., 2002) and PMN–PT systems (Choi et al., 1989; Sing and Pandey,
2001; Ye et al., 2001; Noheda et al., 2002). It is expected that the phase
diagram of the (1–x)PSN–xPT system should show similar features, with the
presence of an MPB region with a curved upper boundary, the complexity of
the phase components and the presence of low symmetry phase(s). Recently,
Haumont et al. (2003) proposed a modified (1–x)PSN–xPT phase diagram
based on the analysis of X-ray and neutron diffraction data. In this phase
diagram, the rhombohedral symmetry was confirmed as a ground state for x
≤ 0.26, while the pure tetragonal symmetry was observed for x ≥ 0.55. A new
monoclinic phase was deduced for 0.37 < x < 0.43. However, the information
for upper boundary of the MPB is missing and no additional anomaly except
the one for T
C
was found in the permittivity measurements as a function of
temperature, which would be associated with the phase transition of the
monoclinic phase. It is well known that two anomalies were detected in the
PMN–PT (Shrout et al., 1990) and PZN–PT (Kuwata et al., 1981) systems
from the measurements of the dielectric permittivity upon cooling,
corresponding to the two transitions: one is the transition from the paraelectric
to the ferroelectric tetragonal phase at T
C
, the other is the transition from the
tetragonal to the ferroelectric rhombohedral or monoclinic phase. Such MPB
behaviour is also expected to occur in the (1–x)PSN–xPT system.
This chapter describes the synthesis, structure, morphotropic phase diagram,
and properties of the (1–x)Pb(Sc
1/2
Nb
1/2
)O
3
–xPbTiO
3
solid solution ceramics
(Section 7.2), and the growth and characterization of Pb(Sc
1/2
Nb
1/2
)O
3
and
(1–x)Pb(Sc
1/2
Nb
1/2
)O
3
–xPbTiO
3
single crystals (Selections 7.3 and 7.4).
7.2 Synthesis, structure, morphotropic phase
diagram and properties of the
(1–
x
)Pb(Sc
1/2
Nb
1/2
)O
3
–
x
PbTiO
3
solid solution
ceramics
In this section, we describe the systematic study of the (1–x)PSN–xPT solid
solution in the form of ceramics with compositions within the morphotropic
phase boundary (MPB) region (0.35 ≤ x ≤ 0.50), in terms of structure and
physical properties. The morphotropic phase diagram has been discussed
WPNL2204
Piezo- and ferroelectric (1–
x
)Pb(Sc
1/2
Nb
1/2
)O
3
–
x
PbTiO
3
177
with the presence of the newly discovered monoclinic phases, providing a
better understanding of the complex MPB behaviour and phase components.
This information is useful for the preparation of the (1–x)PSN–xPT single
crystals for high T
C
piezoelectric applications.
7.2.1 Synthesis of the (1–
x
)Pb(Sc
1/2
Nb
1/2
)O
3
–
x
PbTiO
3
ceramics
Analogue to the synthesis of PMN ceramics proposed by Swartz and Shrout
(1982), the perovskite PSN and (1–x)PSN–xPT ceramics free from pyrochlore
phases were prepared based on the wolframite precursor method (Yamashita,
1993, 1994b; Adachi et al., 1994, 1995). The important steps we used for
synthesis of the (1–x)PSN–xPT ceramics are described here.
Considering that the evaporation of PbO is significantly accelerated when
the temperature is higher than 950 °C, the calcination of the (1–x)PSN–xPT
powder takes place at temperatures below 900 °C and the mixture is reacted
in a closed atmosphere by placing it into an alumina crucible sealed with an
alumina lid.
Our experimental results show that the (1–x)PSN–xPT solid solution
obtained by the calcination process is not always free of pyrochlore phase.
The appearance of the pyrochlore phase is attributed to the relatively low
reaction temperature (< 900 °C) and to the partial loss of PbO, both favouring
the formation of the pyrochlore phase. Therefore, 2–5% excess of PbO out
of total chemical weight is generally added to the mixture prior to the calcining
processing and the weight loss of the mixture is monitored after calcining
and sintering.
The pellets of (1–x)PSN–xPT are sintered in a PbO-rich environment at
1270–1280 °C for 6 to 8 h. The resulting (1–x)PSN–xPT ceramics show a
shrinkage of about 13% in diameter on the average. The formation of a clean
perovskite phase free of pyrochlore phase is verified by the powder X-ray
spectra.
7.2.2 Structural analysis and X-ray spectra of the
(1–
x
)Pb(Sc
1/2
Nb
1/2
)O
3
–
x
PbTiO
3
ceramics
X-ray diffraction (XRD) (Philips, Cu Kα radiation) was performed on the
(1–x)PSN–xPT ceramic pellets of the compositions x = 0.35, 0.37, 0.38,
0.39, 0.40, 0.41, 0.42, 0.45, and 0.50, that were annealed at high temperature;
the spectra are shown in Fig. 7.2. All the ceramics show a clean perovskite
phase free of impurities. The tetragonal splits are visible for the composition
x = 0.45 and these splits become more clear for the composition x = 0.50.
Upon further decrease of the PT content (x < 0.45), a broadened peak with
WPNL2204
Handbook of dielectric, piezoelectric and ferroelectric materials178
asymmetrical profile appears for the cubic (200), (210) and (112) reflections,
which is an indication of the decrease in the structural symmetry.
More detailed analysis is presented in Fig. 7.3 for the pseudocubic (111)
c
and (200)
c
reflections. It is concluded that the major phase adopts the tetragonal
symmetry for x = 0.50 (Fig. 7.3a), with the presence of an additional weak
(minority) phase of different symmetry. The steady growth of the second
phase is clearly revealed in x = 0.45 (Fig. 7.3b), in which the tetragonal
phase is still recognized as the major phase. However, for x = 0.42 (Fig.
7.3c), the tetragonal splitting of (200)
c
becomes less clear, giving rise to a
broadened complex reflection profile, which can be fitted into three peaks.
According to the theoretically calculated characteristic splitting for the different
phases, peaks (1′) and (3′) on the (111)
c
reflection and peaks (1)–(3) on the
(200)
c
reflection indicate the presence of a monoclinic phase, which has
become the major phase in x = 0.42. This monoclinic phase is mixed with
some amount of the tetragonal phase which corresponds to peak (2′) on
(111)
c
and peaks (1) and (3) on (200)
c
that overlap with two of the monoclinic
peaks. This mixture of monoclinic and tetragonal phases is also found for the
compositions of x = 0.41 to 0.37 (Fig. 7.3d–g), in which both the (111)
c
and
(200)
c
reflections show qualitatively the similar features to x = 0.42.
As x decreases to 0.35 (Fig. 7.3h), the (111)
c
reflection can be fitted into
two peaks that are significantly shifted to lower angles, while the (200)
c
reflection can be well defined by a single peak (plus a broad peak due to
2θ
10 20 30 40 50 60 70 80
(001)
(100)
(101)
(111)
(002)
(200)
(112)
(211)
(202)
(220)
x
= 0.35
x
= 0.37
x
= 0.38
x
= 0.39
x
= 0.40
x
= 0.41
x
= 0.42
x
= 0.45
x
= 0.50
(102)
(210)
7.2
X-ray spectra of the (1–
x
)Pb(Sc
1/2
Nb
1/2
)O
3
−
x
PbTiO
3
ceramics with
compositions around the MPB.
WPNL2204
Piezo- and ferroelectric (1–
x
)Pb(Sc
1/2
Nb
1/2
)O
3
–
x
PbTiO
3
179
x
=0.50
x
=0.45
x
=0.42
x
=0.41
x
=0.39
x
=0.38
x
=0.37
x
=0.35
(111)
c
(200)
c
(2′)
(3′)
(2′)
(3′)
(3′)
(2′)
(1′)
(1)
(2)
(3)
(1)
(2)
(3)
(3)
(2)
(1)
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
2θ (deg.) 2θ (deg.)
37.8 38.1 38.4 38.7 39.0 43.5 44.0 44.5 45.0 45.5 46.0
I
(arb. units)
1.0
0.5
0.0
1.0
0.5
0.0
1.0
0.5
0.0
1.0
0.5
0.0
1.0
0.5
0.0
1.0
0.5
0.0
1.0
0.5
0.0
1.0
0.5
0.0
7.3
Pseudocubic (111)
c
and (200)
c
reflections (open circles) of (1–
x
)Pb(Sc
1/2
Nb
1/2
)O
3
−
x
PbTiO
3
with composition
x
= 0.35, 0.37, 0.38,
0.39, 0.41, 0.42, 0.45, and 0.50 at room temperature, and the
deconvolution of the peak profile with different phase components.
The fitting profile, the curves after deconvolution and the residues of
the fitting results are shown together. The vertical lines indicate the
peak positions after deconvolution of the peak profile with
approximate intensity ratios. The pseudocubic reflections (111)
c
and
(200)
c
were fitted to a Lorentzian function. One exception is for the
(200)
c
reflection of
x
= 0.35, which was fitted by a Gaussian function.
The diffracted intensities were normalized with respect to the
maximum of peak intensity in the entire spectrum.
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