Lattice dynamics of perovskite PbxCa1-xTiO 3

Article abstract of DOI:10.1103/PhysRevB.69.184104

Investigation of the structural and vibrational properties of the Pb _xCa_1-xTiO₃ (PCT) system exhibits two phase transitions in the range of x=0-1 by using x-ray powder diffraction and Raman spectroscopy. The first transition occurring at x～0.65 corresponds to the tetragonal-to-cubic phase and the second one occurs near x=0.35 is attributed to the orthorhombic-to-cubic phase. The absence of the intermediate tetragonal phase between orthorhombic and cubic phases (0a decreasing giant LO-TO splitting behavior similar to that exhibited in Pb _xSr_1-xTiO₃ system for lower Pb concentration was also observed, which has been attributed to the highly Pb-O covalent bonding to reduce the long-range Coulomb interaction. Comparison of the change of line shapes of A₁ (1TO) mode among three PbTiO₃-based perovskites indicates that the anharmonicity will become more conspicuous due to the larger high-order potential terms of Ba²⁺ and Ca²⁺ substitution than Sr²⁺ substitution for Pb²⁺.

Full text of DOI:10.1103/PhysRevB.69.184104

PHYSICAL REVIEW B 69, 184104 ͑2004͒
Lattice dynamics of perovskite PbxCa1ÀxTiO3
Shou-Yi Kuo
Precision Instrument Development Center, National Science Council, Hsinchu, Taiwan 30050, Republic of China
*
Chung-Ting Li and Wen-Feng Hsieh
Institute of Electro-Optical Engineering, National Chiao Tung University, Hsinchu, Taiwan 30050, Republic of China
͑Received 5 October 2003; revised manuscript received 20 January 2004; published 25 May 2004͒
Investigation of the structural and vibrational properties of the PbxCa1ϪxTiO3 ͑PCT͒ system exhibits two
phase transitions in the range of xϭ0–1 by using x-ray powder diffraction and Raman spectroscopy. The first
transition occurring at xϳ0.65 corresponds to the tetragonal-to-cubic phase and the second one occurs near
xϭ0.35 is attributed to the orthorhombic-to-cubic phase. The absence of the intermediate tetragonal phase
between orthorhombic and cubic phases (0ϽxϽ0.35) may be mostly attributed to the very restricted region in
the PCT system. In addition, a decreasing giant LO-TO splitting behavior similar to that exhibited in
PbxSr1ϪxTiO3 system for lower Pb concentration was also observed, which has been attributed to the highly
Pb-O covalent bonding to reduce the long-range Coulomb interaction. Comparison of the change of line shapes
of A1(1TO) mode among three PbTiO3-based perovskites indicates that the anharmonicity will become more
conspicuous due to the larger high-order potential terms of Ba2ϩ and Ca2ϩ substitution than Sr2ϩ substitution
for Pb2ϩ
.
DOI: 10.1103/PhysRevB.69.184104
PACS number͑s͒: 61.10.Nz, 63.20.Dj, 63.20.Ry
I. INTRODUCTION
diate phase by high-temperature x-ray diffraction. Based on
the high-temperature neutron-diffraction measurements, de-
tailed structural transitions have been reported by Kennedy
et al.13 It is now clear that CTO undergoes at least two, but
probably three, phase transitions at high temperature.
In technical application among various PbTiO3-based fer-
roelectrics, PbxCa1ϪxTiO3 ͑PCT͒ is a promising material for
practical use in piezoelectric transducers for ultrasonic non-
destructive control devices and imaging applications due to
the unusually large anisotropic piezoelectric response.16–19
Although there have been a number of studies on the Ca-
modified PbTiO3 ceramics, most of them focused on the
electric properties, it still lacks for detailed analysis on lattice
dynamics. It has been recognized that the lattice-dynamical
properties should play a key role on ferroelectricity and re-
lated properties.20 Moreover, our earlier studies on
BaxSr1ϪxTiO3 ͑BST͒ and PbxSr1ϪxTiO3 ͑PST͒ systems have
shown that both similar systems exhibit anomalous discrep-
ancy in lattice dynamics.21 Therefore, further systematic
study is needed to clarify lattice dynamics of the PCT sys-
tem.
In the past, the ABO3 perovskite-type oxides have been
extensively studied mainly not only for their technical appli-
cations but also for fundamental research. Their simple crys-
tal structure, and the variety of structural phase transitions
which they display, make them suitable for experimental
study and for testing theoretical models.
There is great progress in understanding the lattice dy-
namics, dielectric properties, and phase-transition phenom-
ena of oxide perovskite using first-principles calculations
during recent years.1–4 The relatively simple sequences of
phase transitions in PbTiO3 , BaTiO3 , KNbO3, and SrTiO3
have been reproduced using Monte Carlo simulations,
whereas the complex sequences in CaTiO3 ͑CTO͒ have not
yet been successfully reproduced.5
The prototype perovskite structure is cubic (Pm3m,O1h),
but the structure of CTO at room temperature is orthorhom-
16
2h
bic with a quadrupled unit cell (Pbnm,D ).6–8 Although
the deviations from the cubic are small, the crystal keeps its
pseudocubic character with cell parameters down to low tem-
perature. The first evidence of a high-temperature phase tran-
sition was found in the 1940s,9 but the problem of high-
temperature structures has recently been the subject of
intense study.10–13 Earlier studies on phase transition of pure
CTO were investigated by high-temperature x-ray diffraction
͑XRD͒, which shows the orthorhombic distortion of CTO
decreases as the temperature increases, but failed to reach
high enough temperature to directly observe a transition to
higher symmetry.14,15 Neutron diffraction was employed by
Vogt et al.10 to find a direct transformation from orthorhom-
bic to cubic, without intermediate tetragonal phase. More
recently, Redfern,11 by in situ x-ray diffraction, presented
experimental evidence for the existence of an intermediate
tetragonal phase between orthorhombic and cubic structures.
Matsui et al.12 have also found the presence of an interme-
Foster et al.22,23 have first reported the anharmonicity for
the A1(1TO) mode of PbTiO3 consisting of four subpeaks,
and similar behavior were also found in Nd-modified lead
titanate and lead zirconate titanate ceramics.24,25 They advo-
cated that the A1(1TO) mode has a double-well potential in
the ferroelectric state and the anharmonicity of the double-
well potential is the origin of the observed subpeak structure.
In contrast to the earlier studies of slight A and B cation
substitutions,24,25 here, we discuss the effect of isovalent A
cation substitutions of PbTiO3. From XRD measurements,
the variations of lattice constants were calculated for the
polycrystalline PbxCa1ϪxTiO3 powders with x varying from
0 to 1. In addition, Raman spectroscopy provides an in situ
observation of structural changes. The phase transitions dif-
fering from CaTiO3 and CaxSr1ϪxTiO3 systems are charac-
0163-1829/2004/69͑18͒/184104͑6͒/$22.50
69 184104-1
©2004 The American Physical Society

SHOU-YI KUO, CHUNG-TING LI, AND WEN-FENG HSIEH
PHYSICAL REVIEW B 69, 184104 ͑2004͒
FIG. 2. The lattice constants a, b, and c of PbxCa1ϪxTiO3 after
Rietveld refinement. The figures indicate the material is tetragonal
for xϾ0.65, cubic in the region 0.35ϽxϽ1.65 and orthorhombic
while xϽ0.35.
FIG. 1. Powder XRD patterns of PbxCa1ϪxTiO3 samples with
various x values.
terized. Detailed analyses on lattice dynamics are discussed
by applying the anharmonic approximation.
XRD patterns indicated that the material is tetragonal for x
Ͼ0.65, cubic in the region 0.35ϽxϽ0.65, and orthorhombic
while xϽ0.35.
II. EXPERIMENT
In contrast with earlier studies of phase transitions on
CaTiO3 and the related materials, it can be seen that no in-
termediate phases were resolved in our analysis. From the
detailed Rietveld analyses of CTO powder neutron-
diffraction data acquired at high temperature, Kennedy
et al.13 have observed an intermediate tetragonal structure
forming near 1500 K and the primitive cubic structure above
1580 K. The existence of intermediate tetragonal phase was
found in several researches on CaxSr1ϪxTiO3 as well.27–29 It
has been well known that CTO belongs to orthorhombic
phase at room temperature (ϳ300 K). According to the
structural phase transitions on CTO by Kennedy et al.,13 the
region of tetragonal-to-cubic transition only occupied 6% of
the orthorhombic-to-cubic transition while the temperatures
were increased from room temperature to forming cubic
phase. From our XRD analyses, it reveals that PCT system
exhibits different structural transitions from pure CaTiO3 and
CaxSr1ϪxTiO3 systems. More data taken by finer stoichiom-
etry steps in the immediate vicinity of the orthorhombic-to-
cubic transition did not show the intermediate phase either.
Hence, the disappearance of the tetragonal phase between
orthorhombic and cubic phases in the PCT system may be
attributed to the limited stoichiometry region.
The Raman spectra of PbxCa1ϪxTiO3 polycrystalline
powders taken at room temperature are plotted in Fig. 3 for
various x values. As x decreases from 1 to 0.65, the phonon
modes have remarkable changes in their line shapes. Also,
these peaks not only show evidently frequency shift but also
weakens or disappears when xϽ0.65. The observed Raman
spectra became noisy when xϽ0.65. It is interesting to note
that PbxCa1ϪxTiO3 undergoes a phase transition from ferro-
electric to paraelectric phase when xϳ0.65. Besides, the Ra-
man spectrum of our PbTiO3 sample coincides with the ear-
lier literature, and the phonon modes given in Fig. 4 are
characterized according to those of Foster et al.22,23 In the
paraelectric phase, PbTiO3 is cubic and belongs to the O1h
Sol-gel technique was employed in our experiments for
preparing PbxCa1ϪxTiO3 polycrystalline powders to yield
samples with high composition accuracy and homogeneity.
Lead acetate and calcium acetate dissolved in dehydrated
acetic acid and Ti-isopropoxide were used as the raw mate-
rials. Detailed procedure was similar to that described
elsewhere.21,26 Ceramic pellets of about 10 mm diameter and
1–2 mm thickness were obtained by sintering at 1300 °C for
3 h. In contrast to the conventional solid-state reaction
method, the atom arrangement using sol-gel technique was
determined under gelation at lower temperature. Moreover,
the sintering temperature is far below the melting point of
PCT, thus it provides insufficient energy to cause extra atom
rearrangement to result in lattice relaxation.
X-ray powder diffraction patterns were obtained using a
SHIMADZA XD-5 diffractometer and monochromated high
intensity Cu-k␣ line of 1.5405 Å over the range 20°Ͻ2␪
Ͻ80°. The XRD patterns were then Gaussian fitted to get
the diffraction peaks and widths as described elsewhere.26
Raman spectra were excited using the 488 nm line of Arϩ
laser and analyzed using a SPEX 1877C triple spectrograph
equipped with a cooled charg-coupled device. In addition,
the experimental results of PCT are compared with those of
PST and BST systems to account for the influence of cation
substitution.
III. RESULTS AND DISCUSSION
Shown in Fig.
1 are the XRD patterns of the
PbxCa1ϪxTiO3 samples prepared by the aforementioned sol-
gel processes with various x. The patterns were collected at
room temperature and the structural refinements were then
undertaken with Rietveld program. The lattice parameters
and the denoted structural phases after the best fitted refine-
ment procedure are shown in Fig. 2. Preliminary analysis of
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LATTICE DYNAMICS OF PEROVSKITE PbxCa1ϪxTiO3
PHYSICAL REVIEW B 69, 184104 ͑2004͒
that the Raman selection rule is relaxed ascribed to the dis-
order in unit cells of the polycrystalline. The peaks observed
in the cubic phase were labeled as ‘‘disordered’’ in Fig. 4.
Then, through the displacive ferroelectric phase transition,
PbTiO3 becomes tetragonal with the space group,
C14v(P4mm). Modes in each of the three T1u in the
paraelectric phase split into two modes transforming as A1
ϩE, and the T2u mode splits into two modes transforming as
B1ϩE. All modes are both Raman and infrared active.
Therefore, the optical phonon modes of the ferroelectric
PbTiO3 consist of 3A1ϩB1ϩ4E modes as shown in Fig. 4.
However, the split of T2u into B1ϩE has not been observed,
and the B1ϩE modes were classified as ‘‘silent’’ modes. On
the other side, the Raman spectrum of the other end member,
CaTiO3, are observed in accordance with the results in Refs.
30 and 31. A number of studies have reported infrared and
Raman spectra for CaTiO3.32–36 Actually, 117 vibrational
modes
(⌫vibrϭ7Agϩ8Auϩ7B1gϩ8B1uϩ5B2gϩ10B2u
ϩ5B3gϩ10B3u) are expected for orthorhombic CaTiO3, but
most of these modes cannot be detected because of overlap-
ping of bands and their low polarizabilities. Therefore, inter-
pretation of the data is difficult.
From the Raman spectra displayed in Fig. 3, the Pb con-
centration dependence of the peak positions is clearly shown.
Also, the frequencies of the phonon modes in PCT system
are plot in Fig. 4, and the symmetry assignments established
from the data are labeled along the principal axes. The com-
plete Pb concentration dependence shown in Fig. 4 will al-
low us to clarify the structural variation via frequency degen-
eracy. Moreover, it can be seen clearly from Fig. 3 that the
Raman spectra change gradually so that we can conclude that
there are at least two structural transformations that occurred
in the PCT system. First, a tetragonal to cubic phase transi-
tion was found at composition xϳ0.65 of the PCT powders,
which agrees with the XRD analyses. It has been well known
that PbTiO3 belongs to tetragonal phase at room temperature.
The addition of Ca is used to decrease the tetragonality and
transition temperature. It has become customary to classify
ferroelectrics by the properties of the soft optical modes.
According to the lattice-dynamical theory, of particular, vi-
brational soft modes are expected to be associated with the
phase transitions. The A1(1TO) mode is of special interest,
since it is the softest mode together with the E(1TO) mode.
From Fig. 4, these lowest TO phonon modes gradually soften
and broaden their linewidth with increasing Ca content,
which reflects that the ferroelectric phase becomes unstable.
The mode softening becomes unapparent as the Ca content
reaches 0.4 (xϭ0.6), which suggests that the cubic phase
has been formed in the PbxCa1ϪxTiO3 system.
FIG. 3. Room temperature Raman spectra of PbxCa1ϪxTiO3 for
x between 0 and 1.0.
(Fm3m) space group with one formula unit per unit cell.
There are 12 optical phonon modes at the Brillouin zone
center, which transform as 3T1uϩT2u in the irreducible rep-
resentation. The T1u modes are infrared active and the T2u
mode is silent, neither infrared nor Raman active. Hence, the
broadened spectra observed in the paraelectric phase indicate
In addition to mode softening, the A1(1TO) mode exhib-
its an anomalous line shape in the range 0.7ϽxϽ1. For
uniaxial crystal, e.g., PbTiO3, asymmetric line shape of the
A1͑1TO͒ modes may mainly originate from oblique phonons
and anharmonic nature of the lattice. It was found by Foster
et al.23 that the anomalous line shape of the A1 ͑1TO͒ Raman
peak in PbTiO3 single crystal is not a smooth function but
appears to be a superposition of four subpeaks at room tem-
perature. Although it is impossible to ignore the influences of
FIG. 4. The x dependent phonon modes of the polycrystalline
PbxCa1ϪxTiO3. The dotted symbols represent as-read peaks and
fitting results of E(3LO) and A1(3LO) modes, respectively. The
symmetry assignments of phonon modes are labeled along the prin-
cipal axes while PCT are in tetragonal phase (xϾ0.65), and the
observed peaks in the cubic phase, 0.35ϽxϽ0.65, were labeled as
‘‘disordered.’’ The solid lines are eye-guided to view the tendency
of phonon modes as lowering x from 1.0 to 0.6.
184104-3

SHOU-YI KUO, CHUNG-TING LI, AND WEN-FENG HSIEH
PHYSICAL REVIEW B 69, 184104 ͑2004͒
FIG. 6. The Pb concentration dependence of the subpeak fre-
quencies of the A1(1TO) mode of the PbxCa1ϪxTiO3 samples,
showing the softening behavior and splitting tendency between se-
quential subpeaks as x decreases from 1.0 to 0.7.
implicitly indicates the lowering of bond strength and thus
the softening of phonon frequency. The softening behavior of
A1(1TO) mode has also been observed in undoped PbTiO3
single crystal with increasing measurement temperature.22,23
The frequency of each subpeak is the transition energy be-
tween two corresponding states. Therefore, the spacing be-
tween subpeak frequencies is the difference of their transi-
tion energies. In case of harmonic oscillator, the energy
difference is zero. Thus, the nonzero spacing between sub-
peak frequencies as indicated in Fig. 6 seems to be caused by
the anharmonicity of lattice potential. From the above-
mentioned description, we can conclude that the change of
the broad A1͑1TO͒ feature with decreasing x might be related
to the softening and anharmonic effect of the A1(1TO)
mode. In view of the Landau theory, the potential energy can
be expressed as38
FIG. 5. ͑a͒ Raman spectra measured from PbxCa1ϪxTiO3
samples with xϭ1.0, 0.9, 0.8, and 0.7 together with a peak fitting
for all four spectra. ͑b͒ Schematic representation of the double-well
potential of PbTiO3 illustrating the anharmonic nature of the poten-
tial of the A1(1TO) phonon, where n denote the quantum number.
oblique phonons, multiple subpeaks of the A1(1TO) phonon
were observed in the Nd-modified lead zirconate titanate and
lead titanate ceramics and give qualitative agreement to the
anharmonic potential model as well. Referring to those lit-
eratures, our Raman results do reveal a subpeak structure of
tetragonal A1(1TO)-mode frequencies and it is believed that
the anharmonic model can be used to be an auxiliary indica-
tor on the anharmonicity of A1(1TO) mode.
k
␰
␨
6
⌽ q ͒ϭ
q
2ϩ
q
4ϩ
q ,
Ј
͑1͒
͑
Ј
Ј
Ј
2
4
6
where q is the normal mode coordinate, and k, ␰, and ␨ are
Ј
By including E͑1TO͒ and using anharmonic model to de-
compose the E(1TO) and A1(1TO) modes, we show in Fig.
5͑a͒ the fitting results of the E(1TO) and A1(1TO) modes of
PbxCa1ϪxTiO3 at xϭ1, 0.9, 0.8, and 0.7. The four subpeaks
of A1(1TO) mode labeled 1, 2, 3, and 4, respectively, corre-
spond to the transitions from nϭ0 to nϭ1, nϭ1 to nϭ2,
nϭ2 to nϭ3, and nϭ3 to nϭ4 of the vibrational quantum
states. We illustrate these transitions in Fig. 5͑b͒, where the
energy levels shown in one side of the double well describe
the possible phonon states associated with the A1(1TO)
mode.
Figure 6 shows the Pb concentration dependence of sub-
peak frequencies of the A1(1TO) mode. It is obvious that all
four subpeaks evidently show a softening behavior with de-
creasing Pb concentration although the subpeak 4 changes
less than other subpeaks. Earlier study on x-ray near edge
structure ͑XANES͒ spectra has revealed that the Ca substi-
tution for Pb decreases Pb-O and Ti-O hybridization,37 which
the potential parameters, respectively. This potential energy
has been schematically shown in Fig. 5͑b͒. It should be noted
Ј4
that the negative coefficient ␰ in the q term signifies the fact
that PbTiO3 has a first-order transition character. After a te-
dious transformation procedure of moving the origin of
⌽(q ) to one of the two minima in the double-well potential,
Ј
one can obtain the Hamiltonian operator,39,40
HϭH ϩH ,
͑2͒
Ј
0
where H is the Hamiltonian of harmonic oscillator, and H
Ј
0
is the anharmonic term. To simplify the calculation, we have
taken up to the quartic term to obtain H ϭaqϩcq3ϩdq4,
Ј
where a, c, and d are variables depending on the parameters
k, ␰, and ␨. According to the second-order perturbation
theory, the difference of the subpeak frequencies between
two adjacent vibrational transitions is given by39,40
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LATTICE DYNAMICS OF PEROVSKITE PbxCa1ϪxTiO3
PHYSICAL REVIEW B 69, 184104 ͑2004͒
FIG. 8. Difference between square of A1 ͑3LO͒ and A1(1TO)
phonon frequencies for PbxCa1ϪxTiO3 in tetragonal phase.
is the origin of the successive transitions. According to Hida-
ka’s proposal,41 PBT and PCT should have larger sixthorder
potential term ␨ than PST under the same A cation molar
substitution for Pb2ϩ. Moreover, the tetragonal-to-cubic
phase transition occurs at xϳ0.65 and ϳ0.5 in PCT and PST
systems, respectively. Under the same molar cation substitu-
tion for Pb2ϩ, the well depth of the potential should be larger
in PST than in PCT but smaller than in PBT, which always
possesses the tetragonal phase, to be in agreement with ex-
perimental results. Further, the absolute value of parameter ␰
in PST should become smaller followed by Eq. ͑1͒, while
more Sr content was added to lower the well depth of the
potential enlarged by the smaller ␨ compared with the other
two systems. Based on the qualitative explication stated
above, the anharmonicity nature may become negligible in
FIG. 7. Room temperature Raman spectra for ͑a͒
PbxCa1ϪxTiO3, ͑b͒ PbxBa1ϪxTiO3, and ͑c͒ PbxSr1ϪxTiO3 samples
with x between 1.0 and 0.6.
ប2
2m2␻
c2
ប␻nϪប␻nϩ1ϭ
15
Ϫ6d ,
͑3͒
ͩ
ͪ
2
0
2
0
m␻
where ប␻ is the net difference in the energy eigenvalues
n
between the nth and the (nϪ1)th vibrational state and m the
reduced mass. The addition of Ca content in the PCT system
lowers the Curie temperature to cause phonon softening.
Among the parameters appearing in Eq. ͑3͒, ␻ is expected
0
to have the most prominent Pb concentration dependence to
lead to the increase of the spacing between the subpeak fre-
quencies while lowering tetragonality toward cubic phase. In
Fig. 6, the spacing shows splitting behavior as expected,
which implies the validity of the anharmonic model even
though the spacings are unequal due to higher-order pertur-
bation corrections.22,23
the PST system because of the much smaller ␨ and ͉␰͉ than
those in the PCT and PBT systems as revealed in our experi-
mental results.
Figure 8 shows another important observation associated
with the lattice dynamics, which shows the difference be-
tween square of A1 ͑3LO͒ and A1(1TO) phonon frequencies
for PbxCa1ϪxTiO3 as xϾ0.7. Obviously, the cell dimension
of PbxCa1ϪxTiO3 decreases when x changes from 1 to 0.7 in
Fig. 2. We expect that the shrinkage of lattice would lead to
the giant LO-TO splitting while increase the Ca concentra-
tion. In clear contrast to the repulsion of giant LO-TO split-
ting in BaxSr1ϪxTiO3 system, however, Fig. 8 shows an at-
tractive behavior similar to the PbxSr1ϪxTiO3 system by
reducing tetragonality toward the cubic phase. Here, we con-
clude that the observed decreased LO-TO splitting for
PbTiO3-based compounds might be resulted from the contri-
In order to investigate the influence on lattice dynamics of
various A cation substitutions of PbTiO3, Raman spectra of
PbxBa1ϪxTiO3 and PbxSr1ϪxTiO3 are plotted in Figs. 7͑b͒
and 7͑c͒ for comparison. Similar anomalous line shape was
also found in the PbxBa1ϪxTiO3 system. Contrary to Figs.
7͑a͒ and 7͑b͒, the asymmetric line shape of A1͑1TO͒ mode of
PbxSr1ϪxTiO3 ͑PST͒ in Fig. 7͑c͒ was only observed in the
region of xу0.9, even though PST possesses the tetragonal
phase in the region of xϾ0.5. As previously mentioned, al-
though PCT, PBT, and PST systems have similar perovskite
structures, they exhibit diverse lattice dynamics. The obser-
vation of anharmonicity of A1(1TO) mode reflects directly
the influence of various cation substitutions for Pb2ϩ. It has
been well known that SrTiO3 is quantum paraelectric; on the
other hand, BaTiO3 and CaTiO3 show apparently successive
transitions. Hidaka41 has proposed that the necessary condi-
tion for displacive-type ferroelectrics is that the potential-
energy profiles changes with temperature or pressure. In ad-
dition, it has also been concluded that the larger ␨ parameter
*
bution of Z (A) to the mode effective charge due to the
considerable hybridization of Pb-O bonding. Recently, our
previous theoretical calculations and experimental spectra on
O K-edge XANES ͑Ref. 37͒ have revealed that the partial
substitution of A cation, Pb, by Ca not only decreases O
2p-Pb 6p but also O 2p-Ti 3d hybridization. Furthermore,
the Ti L3,2-edge measurements also find that the off-center
displacement of Ti and ferroelectricity persist up to a Pb
concentration between 0.6 and 0.7.41 These results are con-
sistent with our observations.
184104-5

SHOU-YI KUO, CHUNG-TING LI, AND WEN-FENG HSIEH
PHYSICAL REVIEW B 69, 184104 ͑2004͒
IV. CONCLUSION
observed. By comparing the line shape of A1(1TO) mode
among PST, PBT, and PCT, we have concluded that the an-
harmonicity will become more conspicuous due to the larger
In summary, the phase transitions of PbxCa1ϪxTiO3
samples prepared by sol-gel method have been investigated
from XRD and Raman spectra. From the results of both
XRD and Raman measurements, it indicates that there exist
two obvious phase transitions. The first one occurring at x
ϳ0.65 corresponds to the tetragonal-to-cubic phase. The sec-
ond occurs near xϭ0.35 was attributed to the orthorhombic-
to-cubic phase. Unlike the similar SrxCa1ϪxTiO3 system, no
intermediate tetragonal phase was found between orthorhom-
bic and cubic phases. The absence of the intermediate phase
might be mostly attributed to the very restricted region in the
PCT system. From the Raman results of PbxCa1ϪxTiO3, the
consequences of the change of the broad A1(1TO) feature
with decreasing x has been related to the softening and an-
harmonic effect. Moreover, diverse behavior of the anharmo-
nicity of the A1(1TO) mode in PCT, PST, and PBT were
␨ and ͉␰͉ in PCT and PBT systems. In addition, the phenom-
enon of LO-TO splitting similar to those found in PST sys-
tem was investigated as well. The observed decreasing of
LO-TO splitting as lower Pb concentration from 1 to 0.7 has
been interpreted that the substitution of the A cation, Pb, by
Ca not only decreases O 2p-Pb 6p but also O 2p-Ti 3d
hybridization. We do hope the present study will encourage
theoretical calculation to have further insight into lattice dy-
namics on ABO3 perovskites.
ACKNOWLEDGMENTS
The work was supported by Grant No. NSC 92-2112-
M009-037 from the National Science Council, Taiwan.
*
Electronic address: wfhsieh@mail.nctu.edu.tw
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