Infrared activity in the Aurivillius layered ferroelectric SrBi
2
Ta
2
O
9
M. P. Moret
*
and R. Zallen
Department of Physics, Virginia Tech, Blacksburg, Virginia 24061
R. E. Newnham
Department of Materials Science and Engineering, Pennsylvania State University, University Park, Pennsylvania 16802
P. C. Joshi and S. B. Desu
Department of Materials Science and Engineering, Virginia Tech, Blacksburg, Virginia 24061
~Received 29 September 1997!
Experimental studies were carried out on infrared-active phonons in the Aurivillius ferroelectric SrBi
2
Ta
2
O
9
~SBT!, using reflectivity measurements ~down to 200 cm
21
! and transmission measurements ~down to
100 cm
21
! on crystals, pellets, and thin films. An analysis was done of the contrasting consequences of the
competing orthorhombic and pseudotetragonal symmetries in SBT. Reflectivity results for light polarized in the
ab plane show that the anisotropy in this plane is small in the frequency range from 300 to 1200 cm
21
,
indicating the influence of the approximate tetragonal symmetry. Dielectric dispersion properties were derived
for this polarization (E' c) in this frequency range. The transverse-optical ~TO! and longitudinal-optical ~LO!
frequencies corresponding to the dominant E' c band are 613 and 773 cm
21
, respectively. This strong, high-
frequency band arises from a mode dominated by the motion of the oxygen sublattice; its TO and LO
frequencies yield an oxygen-ion Szigeti effective charge of 2 1.5e. Frequency estimates for the TO ~LO! pairs
of other strong bands are 188~330! and 334(451) cm
21
for E'c, and 610~675! and 780(815) cm
21
for E
i
c.
In addition to the main infrared bands, the main Raman bands of SBT are also reported.
@S0163-1829~98!03010-0#
I. INTRODUCTION
Bengt Aurivillius reported on the structures of the mixed
bismuth-oxide layer-structure compounds in 1949,
1
and the
ferroelectric nature of the Aurivillius phases was discovered
about a decade later.
2,3
In recent years, these materials have
emerged as important candidates for nonvolatile ferroelectric
memories.
4
A 256-kilobyte random-access memory has been
reported by Araujo et al.,
5
using SrBi
2
Nb
x
Ta
22 x
O
9
.
SrBi
2
Ta
2
O
9
~strontium bismuth tantalate, SBT! is an impor-
tant component of the thin-film ferroelectrics currently under
development.
The crystal structure of SBT was investigated in 1973 by
Newnham et al.
6
and in 1992 by Rae and co-workers.
7
The
structure is orthorhombic, only slightly distorted from tetrag-
onal. It consists of perovskitelike (SrTa
2
O
7
)
22
slabs alter-
nating with (Bi
2
O
2
)
11
layers. The stacking axis ~normal to
the layers! is customarily defined as the c axis, with the a
axis being the orthorhombic twofold symmetry axis ~the
polar-axis direction for ferroelectricity!. In this A2
1
am
space-group setting, the orthorhombic c axis coincides with
the symmetry axis of the parent tetragonal structure
(I4/mmm). The detailed structures obtained by Newnham
et al.
6
and by Rae and co-workers
7
differ only slightly, and
both yield a spontaneous a-axis polarization of roughly
10
m
C/cm
2
. The main contribution to the polarization arises
from the off-center position of the Ta
51
ion relative to its
octahedron of surrounding oxygens.
6
In this paper, we present results of experimental studies of
infrared-active lattice vibrations in SrBi
2
Ta
2
O
9
. Raman-
active modes in SBT have been reported for powder
samples.
8
Infrared-active modes in SBT have, to our knowl-
edge, not yet been investigated. Our study includes infrared
measurements on both single crystals and polycrystalline
films.
Experimental techniques are described in Sec. II. Section
III presents a symmetry analysis of lattice vibrations in SBT,
and compares the consequences of the orthorhombic crystal
symmetry with those of the approximate tetragonal symme-
try. X-ray-diffraction data on our samples is shown in Sec.
IV. Section V presents our reflectivity results and discusses
the infrared dielectric dispersion of SBT. The vibrational ei-
genvector and effective charges of the mode responsible for
the main infrared band are analyzed in Sec. VI. Transmission
measurements are presented in Sec. VII, which contains an
inventory of the measured infrared-active phonon frequen-
cies and also includes our measured Raman frequencies for
SBT. A summary is given in Sec. VIII.
II. EXPERIMENT
Two main types of SBT samples were investigated, single
crystals and polycrystalline films. The crystals were grown
from the melt, using the method described in Ref. 6. Crystals
were clear plates with dimensions typically about 23 2
3 0.1 mm
3
. Their large surfaces were perpendicular to the
crystal c axis. The domain orientation in the ab plane was
random, since the crystals were not poled. The polycrystal-
line films were made by a metalorganic solution-deposition
technique using, as precursors, strontium acetate, bismuth
2-ethylhexanoate, and tantalum ethoxide. The procedure is
described in Ref. 9. The solution was spin coated onto a 0.3
PHYSICAL REVIEW B 1 MARCH 1998-IIVOLUME 57, NUMBER 10
57
0163-1829/98/57~10!/5715~9!/$15.00 5715 © 1998 The American Physical Society
Copyright by the American Physical Society. Moret, MP ; Zallen, R ; Newnham, RE ; et al., Mar 1, 1998. “Infrared activity in
the Aurivillius layered ferroelectric SrBi2Ta2O9,” PHYSICAL REVIEW B 57(10): 5715-5723. DOI: 10.1103/PhysRevB.57.5715.
mm-thick optical-quality silicon substrate and annealed at
650 °C for 30 min, yielding a well-crystallized film about
250 nm thick. Measurements were also made on a polycrys-
talline pressed pellet of SBT made by standard calcination
techniques and sintered at 1100 °C for one hour, and on thin
films made by pulsed laser deposition.
10
The infrared measurements were carried out with a
BOMEM DA-3 FTIR spectrometer. A pyroelectric detector
was used to cover the wave number region from 100 to
700 cm
21
; a cooled HgCdTe detector was used from 500 to
2000 cm
21
. Spectra were collected with 4 cm
21
resolution,
with 500 interferometer sweeps added for each spectrum.
Reflectivity measurements were performed on the crystals
and the pressed pellet; transmission measurements were
made on the films.
Other experiments done on these samples include x-ray
diffraction and Raman scattering. The x-ray measurements
were made with a Scintag XDS-2000 diffractometer using
Cu radiation at 1.54 Å. Raman measurements were made
with a SPEX 1403 scanning spectrometer and a Dilor XY
Raman microprobe.
III. SYMMETRY ANALYSIS OF LATTICE VIBRATIONS
IN SBT
SBT is orthorhombic; the space group is A2
1
am ~C
2
v
12
,
number 36 in the standard listing!. The dimensions of the
rectangular parallelepiped unit cell are ~in Å! a5 5.531, b
5 5.534, c5 24.984. This unit cell contains four SrBi
2
Ta
2
O
9
formula units ~56 atoms!. The primitive cell, the smallest
translational unit, is half as large, containing two formula
units ~28 atoms!, since the A2
1
am unit cell is face centered
on the A face and contains two lattice points. The
(SrTa
2
O
7
)
22
perovskite slab, perpendicular to the c axis, is
a double layer of corner-sharing TaO
6
octahedra, with Sr
atoms in the midplane. ~There are many structural similari-
ties between SBT and the bismuth-based ‘‘two-layer’’ cu-
prate superconductor Bi
2
Sr
2
CaCu
2
O
8
.
11
!.
Reasonably informative perspective diagrams of the com-
plex crystal structure of SBT appear in the literature.
12,13
It
should be noted that the unit cell indicated in those diagrams
is invariably ~in a practice dating back to Aurivillius
12
! not
the orthorhombic unit cell but is instead the smaller pseudot-
etragonal unit cell ~with dimensions, in Å, of c5 24.98 and
a5 b53.9155.53/
A
2! that contains two formula units and
corresponds to the approximate I4/mmm (D
4h
17
) symmetry.
The tetragonal unit cell is body centered, containing two lat-
tice points and hence two primitive cells. Thus the pseudot-
etragonal primitive cell contains only one formula unit ~14
atoms!. While the ‘‘approximate tetragonal symmetry’’ thus
provides a nice simplification for visualizing and dealing
with the complex SBT structure, the actual broken-symmetry
aspect corresponding to the true orthorhombic symmetry is
responsible for SBT’s ferroelectricity: the tetragonal struc-
ture allows no polar axis, the orthorhombic structure does. It
is necessary to take cognizance of both symmetries that ‘‘co-
exist’’ in SBT.
In the tetragonal structure, all atoms lie on factor-group
symmetry elements of I4/mmm.
14
The strontiums and the
perovskite-slab midplane oxygens are invariant under all six-
teen I4/mmm symmetry operations.
14,15
In the orthorhombic
structure, all atoms are in general positions of the A2
1
am
space group
16
with the exception of the perovskite-midplane
atoms ~the strontiums and one-ninth of the oxygens!.
17
Those
atoms are on the perpendicular-to-c mirror plane ~m of
A2
1
am!, a symmetry element present in both I4/mmm and
A2
1
am. Adjacent perovskite-midplane strontiums ~or oxy-
gens! are translationally equivalent in the tetragonal struc-
ture, translationally inequivalent in the orthorhombic. Adja-
cent perovskite slabs are translationally equivalent in both
structures. Orthogonal in-the-slab directions ~a and b! are
equivalent by symmetry in the tetragonal structure; they are
different ~a is the polar axis! in the orthorhombic.
The four factor-group operations of orthorhombic SBT
are: 1, the identity; 2
a
, the twofold screw axis parallel to the
a axis; 2
¯
b
, the glide plane perpendicular to the b axis with
glide direction along the a axis; and 2
¯
c
, the mirror plane
perpendicular to the c axis ~2
a
,2
¯
b
, and 2
¯
c
correspond, re-
spectively, to 2
1
, a, and m of A2
1
am!. The phonon sym-
metries correspond to the irreducible representations con-
tained in G, the 84-dimensional representation generated by
the displacements of the 28 atoms in one primitive cell.
18
The decomposition of G yields
G5 22A
1
1 20A
2
1 20B
1
1 22B
2
. ~1!
Subtracting the three acoustic modes yields the symmetry
types of the 81 zone-center optical modes of SBT:
G
opt
5 21A
1
1 20A
2
1 19B
1
1 21B
2
. ~2!
Since the A
1
, B
1
, and B
2
modes are infrared active ~for
E
i
a, E
i
c, and E
i
b, respectively!, 61 infrared frequencies
are permitted. All 81 optical modes are Raman active.
For tetragonal SBT, the primitive-cell representation G is
42 dimensional and there are 10 irreducible representations
for D
4h
symmetry. The decomposition of G yields
G5 4A
1g
1 2B
1g
1 6E
g
1 7A
2u
1 B
2u
1 8E
u
. ~3!
Subtracting the three acoustic modes yields
G
opt
5 4A
1g
1 2B
1g
1 6E
g
1 6A
2u
1 B
2u
1 7E
u
. ~4!
Since the A
2u
and E
u
modes are infrared active, the tetrago-
nal structure permits 13 infrared frequencies.
Table I summarizes the contrasting predictions, vis-a
`
-vis
optical experiments, for tetragonal and orthorhombic SBT.
For light polarized in the ab plane (E' c), only 7 one-
phonon infrared lines are permitted by the tetragonal struc-
ture, compared to 42 for the orthorhombic. The tetragonal
structure is centrosymmetric, so that there is mutual exclu-
sion between infrared and Raman activity. But for the ortho-
rhombic structure, the infrared modes are also Raman active.
TABLE I. Number of infrared and Raman eigenfrequencies ex-
pected for tetragonal and orthorhombic SBT.
Optical experiment Tetragonal Orthorhombic
Infrared (E
i
c)619
Infrared (E' c)742~21 E
i
a,21E
i
b!
Raman ~strongest, aa1bb1cc! 421
Raman ~all! 12 81
5716 57
MORET, ZALLEN, NEWNHAM, JOSHI, AND DESU
The third row in Table I corresponds to Raman lines having
contributions from all the diagonal components: aa, bb, and
cc. These dominant Raman lines arise from the fully sym-
metric modes: 4 A
1g
modes for the tetragonal structure, 19
A
1
modes for the orthorhombic.
For the orthorhombic structure, with its low symmetry
and 28-atom primitive cell, none of the optical-mode eigen-
vectors are symmetry-determined. This is true even for the
tetragonal structure, with its higher symmetry ~16 factor-
group operations! and simpler ~14-atom! primitive cell. In-
structive pictures of some symmetrized coordinates for the
tetragonal structure have been given by Graves et al.;
19
the
actual vibrational eigenvectors are linear combinations of
these.
IV. DIFFRACTION RESULTS
All of the samples studied were checked by x-ray diffrac-
tion to confirm that SBT was the predominant component.
Results for a pressed pellet and a single crystal are shown in
Fig. 1; results on the thin films are given in Ref. 9. The top
and bottom panels of Fig. 1 show diffraction measurements
taken in the usual Bragg-Brentano
u
/2
u
configuration. The
middle panel shows a calculated powder pattern based on the
A2
1
am structure of SBT.
20
The top two panels of Fig. 1 match very closely in both
the positions and relative intensities of the diffraction peaks.
This indicates that the pressed pellet closely approximates
polycrystalline SrBi
2
Ta
2
O
9
with randomly oriented grains.
The strongest peak in both diffraction patterns ~near 29°!
corresponds to the ~115!line; the next strongest peak ~near
32.5°! corresponds to ~200!and ~020!.
All of the peaks observed in the measured single-crystal
diffraction pattern, shown in the bottom panel of Fig. 1, are
attributable to SBT. Fewer peaks appear here than for the
polycrystalline pellet. The two lines ~at 29° and 32.5°! that
dominate the pellet pattern are still present, but the crystal
pattern is dominated by a series of six lines ~21.5°, 28.5°,
36°, 43.5°, 51°, 67.5°! that can all be indexed as (h,k,l)
5 (0,0,l), with the observed lines corresponding to l values
of ~6, 8, 10, 12, 14, 18!, respectively. These results indicate
that the scattering vector ~which, in these measurements, was
normal to the large faces of the platelike crystal! is parallel to
the crystal c axis, consistent with previous work
6
on the
orientation of thin SBT crystals.
V. INFRARED REFLECTIVITY AND DIELECTRIC
DISPERSION
Figure 2 presents results for the reflectivity of a polycrys-
talline pellet and a single crystal of SBT. The range covered
is 200 to 1200 cm
21
. ~The frequency or photon-energy scale
used throughout this paper is in terms of the equivalent wave
number units,
n
5 l
2 1
.! Unpolarized light was used, since
the pellet was a composite of randomly oriented crystallites
and the crystal was too small to allow adequate signal with
the use of a polarizer. The pellet reflectivity includes contri-
butions from all three polarizations, E
i
a, E
i
b, and E
i
c.
Because of the near-normal ~11°! incidence used and the' c
orientation of the crystal platelet, the crystal reflectivity of
Fig. 2 essentially includes contributions only from E
i
a and
E
i
b.
The crystal reflectivity exhibits a high-reflectivity phonon
band ~in old terminology, a reststrahlen band! extending ap-
proximately from 600 to 800 cm
21
. The low-frequency edge
of this high-reflectivity plateau is associated with a strongly
infrared-active transverse-optical ~TO! mode; the high-
frequency edge is associated with the corresponding
longitudinal-optical ~LO! mode. This 600–800 cm
21
TO-LO
band is the dominant feature of the crystal spectrum. It is
FIG. 1. X-ray-diffraction patterns of SrBi
2
Ta
2
O
9
.
FIG. 2. Infrared reflectivity of polycrystalline and single-crystal
SBT. The crystal-platelet surface is perpendicular to the c axis.
57
5717INFRARED ACTIVITY IN THE AURIVILLIUS...
also evident in the reflectivity of the polycrystalline pellet, as
seen in the top panel of Fig. 2. In addition, other features
appear in the pellet spectrum; notably the band at 540 cm
21
,
the sharp drop ending near 680 cm
21
, and the kink near
780 cm
21
.
If the approximate tetragonal symmetry of SBT held sway
over its optical properties in the infrared, then E
i
a and E
i
b
would be equivalent. If this were the case, then the E' c
crystal reflectivity shown in the lower panel of Fig. 2 would
correspond to a pure polarization, derivable from a single set
of optical constants ~such as
e
1
and
e
2
, the real and imagi-
nary parts of the dielectric function!. To test this, the crystal
reflectivity has been compared to a theoretical fit in Fig. 3.
The theoretical curve shown in Fig. 3 is based on the
factorized form of the dielectric function
21–23
«
~
n
!
5«
1
~
n
!
2i«
2
~
n
!
5«
`
)
n
n
LOn
2
2
n
2
1 i
g
LOn
n
n
TOn
2
2
n
2
1 i
g
TOn
n
. ~5!
The factorized form for «~
n
! is more suitable than the
classical-oscillator form, for ionic crystals having strong in-
frared bands with large TO-LO splittings.
22–24
The best-fit
parameters are given in the upper part of Table II. The over-
all fit is quite reasonable. The TO and LO frequencies ob-
tained for the main band are 612 and 773 cm
21
, respectively.
The TO-LO pair at 333 and 451 cm
21
is required to fit the
sharp reflectivity dip and the following edge in the
300–500 cm
21
region. The sharp dip is indicative of a TO
frequency that follows closely on the LO of a nearby lower-
lying mode. ~See, for example, the E'c reflectivity of ana-
tase TiO
2
in Ref. 24.! This circumstance is indeed supported
by the numbers in Table II.
Since the reflectivity data is poor below 250 cm
21
, the
lowest TO frequency in Table II ~listed in parentheses! is not
reliable; it is included only for completeness in specifying
the fit. The low-frequency region will be addressed in Sec.
VII in which our infrared transmission measurements are dis-
cussed.
In the high-frequency region of Fig. 3, it can be seen that
the measured reflectivity shows a small dip ~relative to the
theoretical curve! near 675 cm
21
. We interpret this dip as
arising from an E
i
c LO mode observed as a consequence of
the 11° deviation from normal incidence. With unpolarized
incident light and the c axis normal to the surface ~our ex-
perimental geometry!, it is known that off-normal incidence
will produce a shallow dip in an E' c high-reflectivity pla-
teau at the position of an E
i
c LO mode.
24,25
Support for this interpretation of the weak 675 cm
21
fea-
ture in the crystal reflectivity is provided by the well-defined
675 cm
21
reflectivity edge seen in the polycrystalline pellet
~top panel of Fig. 2!. Attributing this clear feature of the
pellet spectrum to its E
i
c component is consistent with the
assignment of the 675 cm
21
feature to a strong LO edge of
the E
i
c spectrum. This assignment is included in the lower
half of Table II. The other entries given for E
i
c are dis-
cussed in Sec. VII.
The reasonableness of the fit shown in Fig. 3 is evidence
that, at least in the spectral region investigated, the optical
anisotropy in the ab plane is not large. If the reflectivity
spectra for E
i
a and E
i
b were very different, a single «~
n
!
function would not be expected to give a good account of the
observed ~admixed! reflectivity. This approximate isotropy
in the ab plane confirms the influence of the parent tetrago-
nal symmetry described in Sec. III.
Figure 4 shows the dispersion function «
1
and «
2
corre-
sponding to Eq. ~5! and the E' c parameters of Table II. The
signature of the main TO-LO pair ~612 and 773 cm
21
!,
prominent in the center of Fig. 4, has the usual oscillator
features; the peak in «
2
is at the TO frequency, the high-
FIG. 3. Infrared reflectivity of crystalline SBT for E' c. The
solid curve is the experimental data; the dashed curve is the theo-
retical fit described in the text.
TABLE II. TO and LO frequencies of strong infrared modes in
SBT, from reflectivity measurements.
TO
n
(cm
21
)
LO
n
(cm
21
)
g
TO
(cm
21
)
g
LO
(cm
21
) D«
1
«
1
(`)55.5
E' c 612 773 24 39 3.3
333 451 16 57 7.3
~230! 330 ~58! 14 ~17.0!
E
i
c 780 815
~610! 675
~520!~560!
FIG. 4. Dielectric dispersion for E' c, obtained from the
factorized-form fit to the crystal reflectivity.
5718 57
MORET, ZALLEN, NEWNHAM, JOSHI, AND DESU
frequency zero of «
1
is at the LO frequency. For the TO-LO
pair at 333 and 451 cm
21
, these features are somewhat modi-
fied by damping and by the circumstance that they ride on a
strong contribution from the unreliable low-frequency oscil-
lator. For both the 612 and 333 cm
21
TO modes, the peak
extinction coefficients corresponding to Fig. 4 agree fairly
well with those obtained by infrared transmission measure-
ments on thin films ~Sec. VII!.
In Fig. 4, «
1
is seen to attain large values at low frequen-
cies. In fact, these values are not large enough to account for
the static ~or very low frequency! dielectric constant of SBT;
reported values of «
1
(
n
'0) lie in the range from 150 to
300.
2,3,9
The last column of Table II lists the contribution of
each mode to «
1
(0); the incremental increase in «
1
on pass-
ing through each absorption band from high frequency to
low, determined by successive applications of the Lyddane-
Sachs-Teller ~LST! relation.
21
The total yields an «
1
(0) of
33. Low-frequency modes contribute much more than high-
frequency ones ~via the
n
TO
2
in the LST denominator!, and
the lowest-frequency contribution in Table II is incorrect be-
cause, as will be seen in Sec. VII, this TO frequency
(230 cm
21
) in Table II is way off ~too high!. Correcting this
doubles «
1
(0) to 66, much closer to the observed values but
still significantly too low. This means that we are missing
some low-frequency infrared modes.
VI. EFFECTIVE CHARGES AND ION MOTIONS
The atomic masses ~in amu! in SBT are: Sr, 88; Bi, 209;
Ta, 181; O, 16. Since oxygen is so much lighter than the
others, the high-frequency modes should be dominated by
the motion of the oxygens. We expect this to be true of the
high-frequency TO-LO pair at 612 and 773 cm
21
.
The complexity of the SBT primitive cell makes it diffi-
cult to calculate eigenvectors and eigenfrequencies from re-
alistic models. But in ionic crystals, it is not unusual for the
strongest infrared mode to be well approximated by a rigid-
sublattice mode in which all positive-ion displacements are
equal, all negative-ion displacements are equal ~and in the
opposite direction!, and the ratio of the two displacements is
determined by the masses ~the center of mass is stationary!.
26
In this section, we assume that the TO mode at 612 cm
21
corresponds to such a rigid-sublattice mode. Based on this
assumed form for the vibrational eigenvector, we can then
use the measured TO-LO splitting to estimate effective
charges on the ions.
The masses yield a value of 20.166 for x
1
/x
2
, the ratio
of the displacements of the positive ~Sr, Bi, Ta! and negative
~O! ions. The oxygens carry 86% of the kinetic energy, con-
sistent with the identification with the high-frequency infra-
red mode.
Using the approach of Kurosawa
21
and assigning rigid-ion
static charges to the ions ~these charges are assumed to move
with the ions!, we obtain
~
v
LO
2
2
v
TO
2
!
«
1
~
`
!
5 4
p
V
2 1
S
(
e
i
*
x
i
D
2
S
(
m
i
x
i
2
D
2 1
.
~6!
Here
v
TO
and
v
LO
are the angular frequencies of the high-
frequency TO and LO modes, V is the primitive-cell volume,
x
i
is the displacement of ion i, e
i
*
is the ion’s charge, and m
i
is its mass. The quantities on the left side of Eq. ~6! are
determined by our experiments ~the entries in the top rows of
Table III!. On the right side, the x
i
’s are set by the x
1
/x
2
ratio. Charge neutrality and the assumption that all the oxy-
gens have the same charge e
O
*
then leaves e
O
*
as the only
unknown in Eq. ~6!. The result for e
O
*
is 2 3.8e, where e is
the magnitude of the electron charge.
Szigeti’s introduction of the local-field correction
27
in the
case of a cubic crystal reduces e
*
by the factor 3/(«
`
1 2).
SBT is not cubic, but our results indicate that the optical
anisotropy is small in the ab plane. Our reflectivity-fit esti-
mate for «
`
~Table III! is consistent with the value of the
near-infrared refractive index of SBT.
28
Using «
`
to estimate
the Szigeti effective charge for the oxygen ions yields a
value of 2 1.5e. This is reasonable for nominally O
22
ions.
Several assumptions are contained in the picture pre-
sented for the main infrared mode at 612 cm
21
, but the rigid-
sublattice picture holds together fairly well. One assumption
that is not realistic, but is easy to remedy, concerns the mo-
tions of the positive ions. Thus far, ‘‘sublattice’’ has been
interpreted in a naive way for maximal simplification: the
nine oxygen ions form one sublattice, the five positive ions
form the other sublattice. Since their masses ~and charges!
are not all the same, it is unreasonable to lump the positive
TABLE III. Zone-center phonon frequencies ~
n
in cm
21
! in SBT.
Infrared Transmission expts. Reflectivity expts.
TO modes
n
k
n
k
141 2.1
E' c 188 3.0
E' c 335 1.0 333 0.8
E
i
c 545 0.7 ~520!
E' c,E
i
c 614 3.9 612 5.0
E
i
c 787 0.2 780
Raman
modes
28 167 ~s! 250 430 607
58 181 ~s! 324 460 812 ~s!
80 213 ~s! 365 518
57
5719INFRARED ACTIVITY IN THE AURIVILLIUS...
