Lattice Vibration Spectra. LXXV. IR Single Crystal Reflection
Spectra of Sr(C10 3 ) 2
H. D. Lutz and M. Schmidt
Anorganische Chemie I, Universität Siegen, Siegen, Germany
Z. Naturforsch. 47a, 1145
1149 (1992); received August 17, 1992
Polarized infrared reflection spectra of Sr(C10 3 ) 2 single-crystal plates are recorded and analysed
for the frequencies of the transversal and longitudinal optical zone-centre phonon modes and other
oscillator parameters by Kramers-Kronig analyses and both the classical 3 parameter (dielectric
sum-function) and the 4 parameter (factorized form) oscillator-fit methods. The frequencies computed are compared with the results of previous single-crystal Raman studies. Because of the great
distortion of the C 1 0 3 ions (site symmetry C J , no intraionic coupling of the CIO vibrations to
symmetric ( v j and asymmetric (v3) stretching modes occurs. The T O / L O splittings of respective CIO
unit-cell group modes rank like the vector elements of the corresponding CIO bonds with respect
to the crystal axes.
Key words: Strontium chlorate; IR reflection spectra; Oscillator-fit calculations; LO phonon modes.
1. Introduction
2. Experimental
The energies (frequencies) of transversal optical
(TO) and longitudinal optical (LO) phonons of solids
are available from inelastic neutron scattering techniques as well as from IR reflection spectra using
Kramers-Kronig analyses and oscillator-fit procedures, respectively (see for example [1]). In the case of
compounds which crystallize in acentric space groups,
the T O and L O phonon modes can also be established
by single-crystal Raman experiments [2-4], We have
performed such Raman studies on Sr(C10 3 ) 2 single
crystals [3]. However, assignment of the spectra obtained was not unequivocally possible. In order to
confirm and complete these results we recorded polarized single-crystal IR reflection spectra of Sr(C10 3 ) 2
and calculated the T O and L O phonon energies using
the fitting procedures mentioned above [1]. More recent investigations on L O phonons of acentric compounds using both IR and Raman experiments are
scarce (see, for example, Razzetti et al. [5]).
Single crystals as large as 27 cm 3 in size were grown
from aqueous solutions by controlled evaporation at
40 °C [7],
For the IR studies, the crystals were cut to give
plates of about ( 1 2 x 1 2 x 3 ) m m 3 in size. The surface
were (100) and (001) planes, respectively. The orientation of the crystal axes was determined by both X-ray
and optical methods [8].
The measurements were performed at near normal
incidence on a Bruker IFS-114 Fourier transform
interferometer in the range 4 0 - 1 8 0 0 c m - 1 . An aluminium mirror was taken as a reference. Polarized
IR radiation was obtained using gold wire grid-type
polarizers with Polyethylen and KRS5 substrate for
the low and high frequency region, respectively.
The polarized IR reflection spectra were converted
into the dielectric dispersion relations by means of
Sr(C10 3 ) 2 crystallizes in the space group Fdd2-C 2 ^
with Z = 8. X-ray single-crystal structure data are reported in [6], The result of group theoretical treatment
(unit-cell group C 2 v ) is given in Table 1 [6],
Table 1. Unit-cell group analysis of zone centre phonon
modes of Sr(C10 3 ) 2 .
c 2v
n
A,
13
13
14
14
A-.
B,
b2
Reprint requests to Prof. Dr. H . D . Lutz, Anorganische
Chemie I, Universität G H Siegen, W-5900 Siegen.
"T
z
-
X
Y
tij.
%
"I
3
4
4
4
3
3
3
3
6
6
6
6
IR, RA
RA
IR, RA
IR, RA
n, total amount of irreducible representations; nT, translations; nT, translational modes; nx, internal (stretching and
bending) modes of the C10 3 ions.
0932-0784 / 92 / 1100-1145 $ 01.30/0. - Please order a reprint rather than making your own copy.
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1146
H. D. Lutz and M. Schmidt • Lattice Vibration Spectra. LXXV
nal optical phonon frequencies, i.e. coTO and coLO, were
determined directly as oscillator parameters or from
the peak positions of the imaginary parts of the dielectric constant e" and the inverse dielectric constant
— Im(l/e), respectively.
3. Results
Fig. 1. Polarized IR reflection spectra (
, 4 P M oscillator
fit) and dispersion functions (
, e";
, — Im(l/e) of
Sr(C10 3 ) 2 single crystals; A x : (100), E || c; B x : (001), E || a\
B 2 : (001), E || b.
both Kramers-Kronig analyses and oscillator-model
calculations using the classic dielectric sum function
(3 parameter model) as well as the factorized form of
the dielectric function (4 parameter model). Details are
given elsewhere [1, 8]. The transversal and longitudi-
Polarized IR reflection spectra of Sr(C!0 3 ) 2 single
crystals and various dielectric dispersion relations are
shown in Figure 1. Additional spectra and dispersion
functions are given in [6, 8]. The oscillator parameters
and the frequencies of the T O and LO phonon modes
are given in Tables 2 and 3.
The main results obtained are that (i) the T O and
LO phonon frequencies calculated with the 4 parameter oscillator fit model best fit the respective Raman
data (see Tables 3 and 4 and Fig. 2), (ii) the damping
constants yLO are not always larger than yTO as it is
reported in [10] for the one oscillator case (see
Table 2), (iii) the Raman band at 1074 c m " 1 is unequivocally a LO mode of the CIO stretching vibrations, and not a two phonon band as discussed in [3] *,
* The lack of L O modes for the C10 ( 1 ) and C10, 2 ) vibrations in the A t (LO) Raman spectrum of Sr(C10 3 ) 2 discussed
in [3] is due to the small T O / L O splittings of these vibrations
in species A j .
1147 H. D. Lutz and M. Schmidt • Lattice Vibration Spectra. LXXV
Table 2. Oscillator parameters ( c m - 1 ) of the zone-centre
phonon modes of Sr(C10 3 ) 2 obtained from IR single-crystal
reflection spectra by the 4 parameter oscillator fit method.
4n Qa
A,
100
120
140
160
[cm"1]
Fig. 2. Oscillator fit of a polarized FIR reflection spectrum
(E || c) of a (100) face of Sr(C10 3 ) 2 ;
, 4 P M model;
, 3 P M model.
and (iv) the T O / L O splittings of the CIO stretching
vibrations mainly reflect the vector elements of the
CIO bonds with respect to the crystal axes (see Table 5),
i.e. the band intensities, which are expected on the
assumption that the vibrations of the three CIO arms
of the CIO3 ions are intraionically uncoupled [3].
Assignment
82
109
128
137
158
191
511
616
893
1029
8.9
29.8
16.5
16.1
14.7
23.2
4.4
10.2
10.0
21.4
86
114
133
147
174
228
517
625
894
1078
9.9
23.8
12.6
18.3
9.6
19.6
5.3
10.5
9.8
13.7
T'
R
R
R
T'
T'
^(C103)
"(Cio3)
V
(Cl-Ou)>
V
(Cl-0(3))
£
co = 2.54
1.89
2.54
0.34
0.25
0.47
82
107
145
163
200
18.4
15.0
10.4
9.8
26.7
88
130
153
172
227
17.1
12.5
9.4
10.6
27.9
T'
T' ?
R
T' ?
0.04
0.02
0.03
0.34
0.15
0.01
476
517
624
905
947
1022
4.3
6.8
8.9
11.2
10.8
18.5
478
519
627
929
1007
1028
5.5
7.9
9.0
7.8
14.6
24.3
^(C103)
V103)
"(C103)
V
(C1-0(1,)
V
(CI-0,2,)
V
(Cl-0,3))
B,
= 2.57
T
r
13.2
0.77
0.80
0.57
0.57
0.42
36
63
122
135
144
181
7.4
19.2
10.5
10.9
12.5
20.2
56
73
127
139
162
209
9.1
25.0
8.6
9.9
15.3
13.7
T
T
0.01
0.05
0.05
0.18
0.00
0.18
475
518
624
911
960
1031
5.4
5.2
8.2
8.3
8.1
13.6
476
523
629
934
960
1076
5.8
5.5
9.9
8.1
8.5
10.7
^(ClOj)
^(cio3)
"(C103)
v<ci-o
, n - (1))
V
(Cl-0(2))
V
<Cl-0(3))
4. Discussion
The results obtained confirm the recent findings [1]
that, owing to the strong distortion of the CIO J ions
in Sr(C10 3 ) 2 , intraionic coupling of the CIO stretching vibrations to a symmetric and two asymmetric
ones does not occur. The vector element of a hypothetical symmetric CIO stretching mode ( v j would be
largest with respect to the c axis of the structure, i.e.
42.67 compared to 17.64 and 34.75 with respect to the
a and b axes, respectively, and, hence, the lowest energy CIO stretching mode, which would be the symmetric one in the case of undistorted CIO3 ions,
should possess the greatest intensity and T O / L O splitting in species Al. This is not the case, as shown in
Fig. 1 and Table 2.
However, there are two findings which cannot be
interpreted so far. (i) The T O / L O splitting (and the
y LO
£oo=2.37
1.03
0.99
0.85
0.50
0.56
0.47
0.06
0.07
0.01
0.22
B,
VTO
a
4nQj = £x(a>l0.—a>j0j)/(Oj0. Ü
k= 1
k* j
R
R
R
(o)l0k-o)l0j)/((o$0k-(D*0j)
[1,9]. (For comparison with experimental 3 P M data see [8].)
b
R, T', (5, v, librational, translational, bending and stretching
modes, respectively; assignment of the librations and translational modes (lattice vibrations) is only tentative.
intensity) of the C10 (2) band of species B 2 are too
small compared to the corresponding vector element
(see Table 5). This too small T O / L O splitting may be
caused by unit-cell group interaction effects (interionic
coupling) or by partial intraionic coupling of the respective CIO vibrations in the case of the mode under
discussion, (ii) The oscillator strength of the C10 ( 1 )
1148
H. D. Lutz and M. Schmidt • Lattice Vibration Spectra. LXXV
Table 3. T O and LO phonon energies of the C10 3 internal vibrations (species A t ) of Sr(C10 3 ) 2 obtained from both
single-crystal Raman spectra and IR reflection measurements (peaks of the dispersion relations of the imaginary part of the
dielectric constant e" and the dielectric loss function — Im(l/e), evaluation procedures see [1]); data of species B; and B 2 see [8].
KKA
a
3 PM
e"
OJ
— Im(l/e)
TO
512
615
893
1031
a
517
625
895
1077
b
4 PM
e"
— Im(l/e)
e"
°ho
(»LO
°ho
517
625
893
1079
511
615
893
1029
Kramers-Kronig analysis. parameters (see Table 2).
b
c
Raman data [3]
— Im(l/fi)
511
615
893
1029
481
511
620
898
959
1023
a
475
516
623
899
944
1021
w LO
W
RO
476
517
624
905
947
1022
478
519
627
929
1007
1028
(Oto
511
616
893
1029
3 Parameter oscillator-fit method. -
B2
Raman d
W
TO/WLO
IR
OP
coTO
517
625
893
1077
Table 4. T O and L O phonon energies ( c m - 1 ) of the internal
CIOJ vibrations (species A 2 , B t , and B 2 ) obtained from
single-crystal Raman spectra [3] and IR reflection measurements (oscillator parameters of the 4 P M oscillator-fit calculations, see Table 2).
A7
B,
Raman Raman
0}JO
d
c
517
625
894
1078
W
LO
510
615
516
622
1021
1074
-
4 Parameter oscillator-fit method. -
d
Oscillator
b a n d of species B j is t o o l a r g e c o m p a r e d t o t h e T O /
L O s p l i t t i n g of t h i s b a n d (see T a b l e 5).
T h e unit-cell g r o u p s p l i t t i n g of t h e C I O s t r e t c h i n g
m o d e s (see T a b l e 6) a r e d i f f e r e n t f o r t h e v i b r a t i o n s of
t h e t h r e e C I O a r m s . T h e f r e q u e n c i e s of t h e v a r i o u s
m o d e s r a n g e B 2 > Bx > A 2 > A l f o r t h e C 1 0 ( 1 ) m o d e s ,
IR
A»TO
475
475
520
518
627
624
892
911
962
960
1024, 1074 1031
«LO
476
523
629
934
960
1076
B
1
>B
2
«A
2
>A
1
for the C 1 0 ( 2 ) ones, a n d
B2%
A j > Bx « A 2 for the C 1 0 ( 3 ) vibrations. T h e m a x i m u m
unit-cell g r o u p s p l i t t i n g s r a n g e ^ v 0 0 ( i ) > < d v C I O r | «
z l v a 0 ( 3 ) . T h e s e d i f f e r e n t unit-cell g r o u p s p l i t t i n g s c a n
b e r e a l i z e d by t h e d i p o l e - d i p o l e i n t e r a c t i o n m o d e l . As
b a s i s of t h i s d i s c u s s i o n , t h e h y p o t h e t i c a l p h o n o n fre-
oblique phonons [3].
Table 5. Vector elements (pm) [3] of the CIO arms of the C 1 0 3 ions with respect to the crystal axes of Sr(C10 3 ) 2 (VE) and
both T O / L O splittings ( c m - 1 ) and oscillator strengths (OS) (see Table 2) of the respective CIO stretching vibrations (CIO
bond lengths (pm) [6] in parentheses).
C10 ( 1 )
x
y
z
(Bj)
(B 2 )
(A,)
(150.7)
C10 ( 2 )
(147.4)
C10 ( 3 )
VE
TO/LO
OS
VE
TO/LO
OS
98.2
106.9
40.6
24
23
9
0.340
0.183
0.072
123.6
73.2
33.1
60
0
1
0.149
0.003
0.009
Table 6. Unit-cell group splittings of the CIO stretching
modes ( c m - 1 ) of Sr(C10 3 ) 2 (the hypothetical phonon
frequencies to 0 are calculated with the equation u>l =
(2co* 0 + a>£ 0 )/3[ll]).
Species
cio(1)
cio(2)
cio(3)
A,
A2
B,
B2
Mean values
of a>0
893
898
913
919
945
959
967
960
1046
1023
1024
1046
906
958
1035
(145.8)
VE
27.5
76.0
120.5
TO/LO
OS
6
45
49
0.005
0.180
0.221
q u e n c i e s co 0 , w h i c h a r e a f f e c t e d n e i t h e r by t h e local
field £ l o c n o r b y l o n g - r a n g e electric f o r c e s [11], a r e
c h o s e n (see T a b l e 6).
T h e C I O 3 b e n d i n g m o d e s a r e strongly intraionically
c o u p l e d . A d e t a i l e d i n t e r p r e t a t i o n of t h e s e m o d e s , f o r
w h i c h co 0 p h o n o n f r e q u e n c i e s m a y b e c a l c u l a t e d in t h e
s a m e m a n n e r a s f o r t h e s t r e t c h i n g m o d e s , in t e r m s of
intensities, T O / L O
splittings,
and
unit-cell
group
s p l i t t i n g s is t h e r e f o r e n o t s t r a i g h t f o r w a r d . T h e s a m e is
true for the lattice m o d e s (translational
vibrations)
1149 H. D. Lutz and M. Schmidt • Lattice Vibration Spectra. LXXV
a n d l i b r a t i o n s of t h e C I O 3 i o n s in the l o w - f r e q u e n c y
T h e a u t h o r s a r e g r e a t l y i n d e b t e d t o P r o f . D r . S.
r e g i o n of t h e s p e c t r a . F o r t h e a s s i g n m e n t of these
Haussühl, Univ. Cologne, for providing
m o d e s see T a b l e 2.
monocrystals.
[1] J. Himmrich, G. Schneider, J. Zwinscher, and H. D. Lutz,
Z. Naturforsch. 46a, 1095 (1991).
[2] R. Claus, L. Merten, and J. Brandmüller, Light Scattering by Phonon-Polaritons, Springer Tracts in Modern
Physics 75, Berlin 1975.
[3] H. D. Lutz, E. Alici, and Th. Kellersohn, J. Raman Spectrosc. 21, 387 (1990).
[4] V. Lemos, P. A. P. Gomes, F. E. A. Melo, J. Mendes
Filho, and J. E. Moreira, J. Raman Spectrosc. 20, 155
(1989).
[5] C. Razzetti, P. P. Lottici, and R. Bacewicz, J. Phys. C 15,
5657 (1982).
Sr(C103)2
[6] H. D. Lutz, W. Buchmeier, E. Alici, and W. Eckers,
Z. Anorg. Allg. Chem. 529, 46 (1985).
[7] S. Haussühl, private communication.
[8] M. Schmidt, Doctoral Thesis, Univ. Siegen 1992.
[9] L. Merten and G. Lamprecht, Phys. Stat. Sol. 39, 573
(1970).
[10] R. P. Lowndes, Phys. Rev. B 1, 2754 (1970).
[11] P. Grosse, Freie Elektronen in Festkörpern, SpringerVerlag, Berlin 1979, pp. 212 ff.