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Infrared and Raman spectra and normal coordinate calculations on trirutile-type compounds
0584-8539/81/070487-09$02.00/0 0 1981 Pergamon Press Ltd.
Spectrochimica Acre. Vol. 37A, No. 7, Pp. 487-495, 1981. Printed in Great Britain.
Infrared and Raman spectra and normal coordinate calculations on trirutile-type compounds H. HAEUSELER Universitat
Siegen, Laboratorium
fur Anorganische Chemie, D 5900 Siegen 21, Federal Republic of Germany (Received
10 October 1980)
Abstract-The Raman and i.r.-spectra of trirutiles AB206 with A = Mg, Zn, Ni, Co and B = Sb, Ta and A;TeO, with A’ = Al, Ga, Cr, Mn, Fe have been recorded on powder samples. For the trirutile-type structure Cartesian symmetry coordinates are given. Based on these coordinates a normal coordinate and force constant calculation has been performed. The Te-0 stretching force constant has a value of 3.1 mydn A-’ which corresponds to the value predicted for a covalent single bond. The normal modes are discussed in relation to the potential energy distribution and to the vibrations of a free octahedron. Correlation snlitting for the Raman-active octahedral vibrations of
species A,, and II:, is computed to be very s&all INTRODUCTION
Numerous ternary oxides, tantalates MTa,O, and antimonates MSb206 of divalent metals Zn, Mg, Ni, Co and Fe and tellurates M,Te06 of trivalent metals Al, Ga, Cr, Mn, Fe and Rh and chromiumtungstate (Cr2WOs) crystallize in the trirutile-type structure. The i.r.-spectra of the antimonates have been investigated and assigned by FRANCK et al.[l] in the region 1000-40 cm-‘. HUSSON et al. [23 reported very recently on the i.r. and Raman spectra of the antimonates and tantalates in connection with a force constant calculation. The i.r. spectrum of Cr,WO, has been reported by CLARK et al. [3]. The i.r. spectra of the tellurates are only known in the region 1000-430cmrecorded with very low resolution[4]. No previous data are available on the Raman spectra of the tellurates. We will therefore present in this paper the i.r. and Raman spectra of the tellurates along with a force constant calculation on Ga2Te06 and our results on the Raman spectra of the antimonates and tantalates. EXPERIMENTAL The samples were prepared using the methods described in the literature [3-71. X-ray diffraction patterns Table 1. Unit cell dimensions
F
Antimonates
r-
were obtained from a Huber Guinier powder chamber 621 using CuKa, radiation. The photographs were calibrated internally with quartz, and the unit cell dimensions (Table 1) were refined by a least-squares procedure. Infrared spectra were recorded down to 200cm-’ on Perkin-Elmer grating spectrometers PE 325 and PE 580 using CsJ pellets and down to 40cm-’ on Bruker i.r. Fourier spectrometer IFS 114 using Nujol mulls on polyethylene. Raman spectra were obtained from powder samples on a Coderg T 800 Raman spectrometer (90” scattering geometry) using an argon ion laser (488 or 514.5 pm). INFRAREDAND
RAMAN SPECTRA
The i.r. and Raman spectra of some antimonates and tantalates have been published by HUSSON et al. [2]. The ir. data are in good agreement with our results, but in the Raman spectra there are differences concerning the frequencies of the vibrations and the number of observed Raman lines. Therefore we present our results on the Raman spectra of the antimonates and tantalates (see Figs. 2 and 3). Figures 4 and 5 show the i.r. and Raman spectra of some tellurates. The very poor Raman spectra of Cr,TeO, and Fe2Te06 are due to the dark colour of the samples. Perhaps better results could be obtained by using a red excitation line. [pm] of the investigated
trirutiles Tellurates
Tantalates
a0
c
o
@3Ta&j
A12Te06
444.7(l)
870.9(l)
NiSb206
NiTa206
Ga2Te06
454.6(l)
896.9(l)
CoSb206
CoTa206
Cr2Te06
454.7(l)
901.4(l)
FeSb206
Fe2Te06
460.6(l)
909.6(l)
ZnSb206
Mn2Te06
460.7(3)
911.9(9)
Wb206
487
H. HAEUSELER
488
According to the group theoretical analysis[l] there are for the trirutile-lattice at wavevector k = 0 12 i.r. active and 16 Raman active vibrations, all of which cannot be observed in the spectra. Especially the Raman spectra are not complete in most cases. For the interpretation of the spectra we have to consider two cases: (i) the antimonates can be regarded as to be built from units containing two Sb06 octahedra sharing an edge. These Sb,O,,units are linked by common vertices. The twovalent metal atoms occupy the resulting octahedral holes. The same description is possible for the tantalates. (ii) The tellurates and tungstate, on the other hand-sometimes referred to as inverse trirutiles-contain isolated TeO, and W06 octahedra, respectively. According to the normal coordinate calculations by HUSSON et a/.[21 the spectra of the tantalates and antimonates are dominated by the vibrations of the TatOlo and Sb20,, units, respectively. The participation of the two-valent metal atoms is very small. Only two i.r. active vibrations seem to be mainly vibrations of the M’*06 octahedron. These results cannot be transferred to the tellurates where tellurium occupies lhe same site as the two-valent metal atoms in the antimonates since there must be significant changes in the force constants and therefore in the assignment of the vibrations. In these compounds the high frequency absorptions should be due to the isolated Te06octahedra. Table 2 gives the correlation between the symmetries of the vibrations of a free TeO,octahedron to TeO,-octahedra under site group and unit cell group symmetry, respectively.
Fig. 1. Unit cell of GazTe06. 1,2 = Te; 3-6 = Ga; 7-18 = 0. The numeration of the atoms corresponds to Table 2.
SYMMETRYCOORDINATES
The ternary oxides of trirutile-type crystallize tetragonal (space group P4Jmnm-Dg) with two formula units per unit cell. The structure can be regarded as a superstructure of rutil type with an ordered distribution of the metal atoms on the titanium sites resulting in a tripling of the c-axis (Fig. 1). There are 18 atoms in the primitive cell resulting in a total of 51 vibrational modes. These modes have the irreducible representation [l] I = 4A,, +2A2, + 2B,, + 4B2, + 6E, + A,, + 4A2, + 5B,, + Bzu + 8E,,. The vibrations of species A,,, B,,, Bzg and E, are Raman-active, the modes with symmetries Azu and E. are i.r.-active. Based on Cartesian coordinates we have deduced Cartesian symmetry coordinates for all vibrations of the trirutile-lattice (see Table 3). From the symmetry coordinates one can see that the divalent metals in the tantalates and antimonates and the tellurium or tungsten in the tellurates and tungstate does not take part in all the Raman-active vibrations.
11
I
200
Fig.
2. Raman
I
400
I
I
600
I1
I
I
800
cm-’
spectra of some antimonates trirutile-type structure.
with
Infrared and Raman spectra and normal coordinate calculations
489
.5 b
-8
-B
-H -8 3s
8
-8 ‘E
I-
H. HAEUSELER
490
Table 2. Correlation diagram for the vibrations of the Te06octahedron under site group and unit cell group symmetry ibration
free octahedron
site group
“2
_-
/g------_
Eg ------I
A
yA1g B29
/
*29
Y
*1!3
Big-----A__ *
Ag-----B O5
-
FORCE FIELD AND FORCE CONSTANT CALCULATIONS
FOR Gs,TeO,
Following WILSON’S GF matrix method [9] extended for the treatment of lattice vibrations by SHIMANOUCHI et a/.[101 we have chosen a modified valence force field with 12 force constants: two Te-0 valence force constants j, and jZ corresponding to the two different Te-0 distances in the TeOs-octahedra, 3 Ga-0 valence force constants j3, j., and f5 corresponding to the various Ga-0 distances in the Ga,Olo units of the trirutile structure. For the interpretation of the absorptions especially in the long wavelength region we need furthermore some angle bending coordinates in the Te06 octahedron (j6, j,, j8) and in the GazOlo unit cfg, f~o, jr,, jr& For the number of the corresponding internal coordinates in the primitive cell and the interatomic distances and angles between the concerned atoms see Table 4. Since the Raman spectrum of Ga,TeO, is not complete and we could not exactly assign the Raman lines to the different Raman-active species we decided to do the force-constant calculations on the basis of the 12 i.r. frequencies only. Therefore we restricted for mathematical reasons our force field such that we used the following relations between the force constants: j, = j2, j3 = jd = j5, f6 = f, = f8 and jg = jlO. This means that we
unit cell group D4h
D2h
Oh
B29 -._ B3g 1
29 2Eg
used a set of 6 force constants for the interpretation of the vibrational spectra. Force constant calculations were carried out with the CDC Cyber 76 of the RRZ Cologne using a computer program the program LSMX by based on SHIMANOUCHI[l 11. The agreement between observed and calculated frequencies was checked by the function h=
c 2
(vci -
I.
~oi)*
n
The obtained values for the force constants are given in Table 4. The observed and calculated i.r. frequencies are presented in Table 5 along with the observed and calculated Raman frequencies, the assignment of the modes, and the potential energy distribution for the force constants.
DISCUSSION
For the obtained set of force constants (see Table 4) there is relatively good agreement between the observed and calculated frequencies (see Table 5) of the i.r.-active vibrations. The differences are within 15%. This seems to be good in consideration ot &e strong restrictions placed
Infrared and Raman spectra and normal coordinate calculations
Table 3. Symmetry coordinates
Alg:
S1
=
l
2
(2
3
-
(x, + y, -
s3
(-xl0
= :
+‘16 1 s4 = 2fi
(_Zll
Y8
xg +
-
Yg
+ x10
-
Y*(J)
+ y16 - x17 - Y17 - “18 + y18) + 212 - Z13 + ‘14
- ‘15
- ‘16
- Yll
- ‘17
- x12 - Y12 + Xl3 + Y13 + X14 + Y14 -95
- Y16 - ‘17
+ y17 + ‘18
s
(x7 + Y7 - X8 - Y8 + x9 - Yg - x10 - YlO)
slo= 1 $1 2-P Sll’
;
+ x12 - Y12 - x13 + Y13 - x14 + Y14 - X15 - Y15
+ y16 - ‘17
- Y17 + ‘18
- 212 + 213 - 94
- ‘15
(x3 - x4 - x5 + X6)
s13= ;
(z7 - Z8 + zg - 210)
sl4=2-h
h
S15’&kYll
- 92
s1*
+ ’ 13 - ‘14
- ‘15
- y18) - ‘16
+ ‘17
=;
+ ‘18)
(Y, - Y4 - Y5 - Y6)
- ‘16
+ ‘17
+ ‘18)
+ Y12 - Y13 - Y14 - Y15 - Y16 + Y17 + y18)
s16=2Lfl (‘11
+ z12 - 213 - z14 - z15 + ‘16 S18 = g
517 ‘8 l
(Zl + z2)
S19 = $
(2,
520 = a1
(x I* - Y11 - x12 + Y12 - 93 -‘16
-1 s kll 21 -27T 522 =h
+ Y15
- y18
(23 - z4 - 25 - Z6)
(x4 - Yll
- ‘18)
+ YlO)
s7 = $ =1 2fl
compounds
+ Yll - x12 + Y12 + x13 - Y13 + x14 - Y14 - x15 + Y15
(-x*1
+‘16
E’ ”
26)
-
S6 = :
sg = :
A2”
-
(x7 - Y, - x8 + Y8 - ‘9 - Yg + ‘10
8
E : g
X8
55 = ’ nff
+‘16 829 :
+ 15
s* = !
2lF
81g:
24
for the vibrations of trirutile-type
491
- ‘17
(23 + 24 + 25 + z6)
+ 28 + zg + ZlO)
- Y16 - ‘17
- Y17 + ‘18
+ Y13 + x14 - Y14 + ?5
+ z12 + z13 + z14 + z15 + ‘16
+ ‘17
‘23
=a l
(Yl - Y2)
(x 3 t x4 + x 5 + ‘6)
‘25
=3
(Y,
l = ;T
‘26
=i
‘28
=2-$(xl1
(x7 + X8 + xg +qo)
+ Xl2 + x13 + xl4
s2g =2Lfl C-Y11 -Yl2 530 =2Lfl(z11
s2, = $
+ Y15
+ y18)
(Xl + x2)
‘24
+ ‘18
+ ‘18)
+ Y4 - Y5 - Y6)
(Y, + y8 - Yg - YIOI
+ x15 + ‘16
+ ‘17
+ ‘18)
- Y13 - Y14 + Y15 + Y16 + Y17 + y18)
- 212 - z13 - 214 + 215 - ‘16
- ‘17
- ‘18)
*For species EBand EMonly one component of the two degenerate coordinates is given. The numeration corresponds to Fig. 1.
H.
492 Table 4. Internal coordinates,
,
internal
force constants, and correspondina interatomic distances and angles _ -
No of internal coordinates
coordinate
Te-0
4
Te-0
8
Ga-0
8
Ga-0
8
Ga-0
8
0-Te-0
16
0-Te-0
4
0-Te-0
4
0-Ga-0
16
0-Ga-0
16
HAELJSELER
force
interatomic
constant
or angle
[mdyn/R]
f1
distance
[I
[degrees]
1.935
3.10
1.921
fZ
1.963
f3
1.967
1.12
f4
1.976
f5
90.00
f6 0.73
f7
80.9’ 99.10
f8 f9
89.4’
0.05
90.6’
f10
0-Ga-0
8
fll
0.19
100.20
0-Ga-0
4
f12
0.47
78.2’
8
on the force field, i.e. the use of only six independent force constants. The value of the Te-0 stretching force constant of 3.1 mdyn A-’ is comparable to the values obtained for the Te-0 bond in some other tellurates with different structures. LENTZ[12] gives a
value of 2.46mdyn A-’ for the Te-0 bond in a tellurate with elpasolite structure, FADINI et al. [ 131 find a mean value of 3.7 mdyn A-’ for some perovskite tellurates and BARAN et al. [14] have calculated the Te-0 force constant to be 3.45 mdyn A-’ in spine1 type compounds. The calculations by
Table 5. Observed and calculated frequencies [cm-‘], assignment, and potential energy distribution for the force constants of GalTe06 IR
Raman PEO
0
Qc
780
771
742 701
species
PED
f1/2
f3/4/5
f6/7/8
Aeu
69
9
3
2
745
Eu
67
19
7
715
Eu
67
20
13
649
642
A2”
-
45
602
584
Eu
22
40
560
578
A2”
1
542
489
Eu
1
373
422
E,
1
5
328
334
At”
8
45
0
f9/10
fll
f12
2
15
-
7
-
-
-
-
49
1
4
1
34
4
-
-
45
50
1
3
-
7
85
5
2
-
86
7
I-
21
5
-
21
20
2
-
‘0
gc species
f1/2
f3/4/5
f9/10
fll
f12
22
-
4
13
26
23
-
4
13
34
30
28
2
3
3
Alg
37
29
26
1
4
3
E g
21
22
49
2
6
-
664
82g
65
19
9
663
Alg
63
19
11
1
1
5
648
Eg
50
25
23
1
1
-
528.
557
Elg
-
-
92
8
-
-
408
464
E g
10
84
I
4
l-
14
14
2
-
750
82g
35
26
749
Alg
34
699
699
82g
690
695 673
791
650
608
f6/7/8
.
115
279
277
E,
8
47
23
249
257
Eu
16
45
4
11
24
-
3C4
290
Eg
1
70
142
121
Eu
2
46
9
40
3
-
298
264
Alg
14
48
7
13
2
16
251
B2g
20
48
11
4
3
14
230
Eg
2
44
4
16
34
-
150
Eg
9
25
1
37
28
-
68
Big
-
-
6
94
-
-
201 140
493
Infrared and Raman spectra and normal coordinate calculations FADINI et al.[13] and BARAN et al.[l41 are based on the assumption of fully isolated TeO, octahedra neglecting all couplings to other parts of the structures. Therefore their values for the TeO stretching force constant may be falsified a little bit. But in conclusion one can say, that the Te-0 stretching force constant is only slightly dependent on the structure,and lies, at least in tellurates with isolated Te06 octahedra, near the value 3.0 mydn k’ that is calculated for a covalent single bond by SIEBERT’Sproduct rule [ 151. As can be seen from the potential energy distribution for the force constants (see Table 5) the three shortwaved modes in the i.r. spectrum (see also Fig. 6) are mainly vibrations of the TeO,-octahedron. This is in accordance with the correlation diagram of Table 2 which predicts that the vj of the octahedron under unit cell group symmetry splits into three components: 1A2, and 2E,, vibrations.
A2o 771
A2u 334
The assignment of the three absorption maxima (see Table 5) obtained by the normal coordinate calculations corresponds with these predictions. The vibrations at 649, 602 and 560cm-’ show strong participation of the Ga-0 stretching constant and the 0-Te-0 angle bending force constant. This means that there is strong coupling of the bending vibration vq of the octahedron with some stretching vibrations in the Ga,OIO unit. Only the two modes at 542 and 373 cm-’ can be regarded as to be of nearly pure bending character. The remaining longwaved i.r.-active modes are more or less strong affected by the force constants in the Ga,O,, polyhedra with only small participation of the Te06 group. The agreement between the observed and calculated frequencies of the Raman-active vibrations is not so good as for the i.r.-active vibrations and the assignment given in Table 5 is only tentative.
Eu 745
Eu 715
A2,,
EU 489
578
EU 277
Eu
257
A2u 642
E,,
422
Eu
121
Fig. 6. Vibrational modes and calculated wavenumbers [cm-‘] of GazTe06 in the i.r.-active species Azu and E..
SAA
Vol. 37A, No. 1-C
H. HAEUSELER
Al9
749
f3zg 664
Eg 464 Fig. 7. Vibrational
Al9
695
Alg
Big
68
B2g
B2g
Eg
251
290
663
750
Alg
BP9
264
699
Eg
673
Eg
648
Eg
230
Eg
150
modes and calculated wavenumbers [cm-‘] of GazTeOc in the Raman-active species A,,, B,,, Bzg and E8
As can be seen from the potential energy distribution (Table 5) the modes of species A,, and Bzr are (see also Fig. 7) mainly vibrations of the TeOs octahedra with mixed stretching and bending character. The small differences between the calculated values of the Al, and Big vibrations (see Table 5) show that correlation splitting for these vibrations is expected to be small. This may be an effect of the restricted force field which includes
only nearest neighbour interactions but on the other hand this could be the cause that the number of observed Raman lines is not in agreement with group theoretical predictions.
REFERENCES [l] R. FRANCK, C. ROCCHICCIOLI-DELTCHEFF and J. GUILLERMET,Spectrochim. Acta 3OA, 1-14 (1974).
Infrared and Raman spectra and normal coordinate calculations [2] E. HUSSON,Y. REPELIN, H. BRUSSETand A. CEREZ, Spectrochim. Acta 35A, 1177-1187 (1979). [3] G. M. CLARK and W. P. DOYLE, Spectrochim. Acta 22, 1441-1447 (1966). [4] G. BAYER, Ber. Dtsch. Keram. Ges. 39, 535-554 (1962). [5] A. BYSTR~M, B. H~K and B. MASON, Arkio Kemi, Miner. Geol. 15B(4), l-8 (1941). [6] F. HUND, Naturwissenschaften 58, 323 (1971). [7] L. DEGUELDRE, Y. GOBILLON, L. BURGEOIS, U.S. 3,736,269; CA 19: P 55561. [8] T. BIRCHALL, J. Solid State Chem. 27, 293-298 (1979). [9] E. B. WILSON, J. C. DECIUS and P. C. CROSS, Molecular Vibrations. McGraw-Hill, New York, Toronto, London (1955).
495
[lo] T. SHIMANOUCHI,M. TSUBOI and T. MIYAZAWA, J. them. Phys. 35, 1597-1612 (1961). 1111 . _ T. SHIMANOUCHI.Computer Programs for IiIormal Coordinate Treatment- of Polyatomic- Molecules, Tokyo (1968). [12] A. LENTZ, J. Phys. Chem. Solids 35,827-832 (1974). 1131 _ _ A. FADINI. I. Joos. S. KEMMLER-SACK.G. RAUSER. H.-J. ROTHER,E. S~HILLINGER,H.-J. SCHIITENHEL~ and U. TREIBER, Z. anorg. allg. Chem. 439, 35-47 (1978). [14] E. J. BARAN and I. L. BOITO, Z. anorg. aHg. Chem. 463, 185-192 (1980). 1151 H. SIEBERT, Anwendungen der Schwingungsspektroskopie in der Anorganischen Chemie. Springer, Berlin, Heidelberg, New York (1966).
Spectrochimica Acre. Vol. 37A, No. 7, Pp. 487-495, 1981. Printed in Great Britain.
Infrared and Raman spectra and normal coordinate calculations on trirutile-type compounds H. HAEUSELER Universitat
Siegen, Laboratorium
fur Anorganische Chemie, D 5900 Siegen 21, Federal Republic of Germany (Received
10 October 1980)
Abstract-The Raman and i.r.-spectra of trirutiles AB206 with A = Mg, Zn, Ni, Co and B = Sb, Ta and A;TeO, with A’ = Al, Ga, Cr, Mn, Fe have been recorded on powder samples. For the trirutile-type structure Cartesian symmetry coordinates are given. Based on these coordinates a normal coordinate and force constant calculation has been performed. The Te-0 stretching force constant has a value of 3.1 mydn A-’ which corresponds to the value predicted for a covalent single bond. The normal modes are discussed in relation to the potential energy distribution and to the vibrations of a free octahedron. Correlation snlitting for the Raman-active octahedral vibrations of
species A,, and II:, is computed to be very s&all INTRODUCTION
Numerous ternary oxides, tantalates MTa,O, and antimonates MSb206 of divalent metals Zn, Mg, Ni, Co and Fe and tellurates M,Te06 of trivalent metals Al, Ga, Cr, Mn, Fe and Rh and chromiumtungstate (Cr2WOs) crystallize in the trirutile-type structure. The i.r.-spectra of the antimonates have been investigated and assigned by FRANCK et al.[l] in the region 1000-40 cm-‘. HUSSON et al. [23 reported very recently on the i.r. and Raman spectra of the antimonates and tantalates in connection with a force constant calculation. The i.r. spectrum of Cr,WO, has been reported by CLARK et al. [3]. The i.r. spectra of the tellurates are only known in the region 1000-430cmrecorded with very low resolution[4]. No previous data are available on the Raman spectra of the tellurates. We will therefore present in this paper the i.r. and Raman spectra of the tellurates along with a force constant calculation on Ga2Te06 and our results on the Raman spectra of the antimonates and tantalates. EXPERIMENTAL The samples were prepared using the methods described in the literature [3-71. X-ray diffraction patterns Table 1. Unit cell dimensions
F
Antimonates
r-
were obtained from a Huber Guinier powder chamber 621 using CuKa, radiation. The photographs were calibrated internally with quartz, and the unit cell dimensions (Table 1) were refined by a least-squares procedure. Infrared spectra were recorded down to 200cm-’ on Perkin-Elmer grating spectrometers PE 325 and PE 580 using CsJ pellets and down to 40cm-’ on Bruker i.r. Fourier spectrometer IFS 114 using Nujol mulls on polyethylene. Raman spectra were obtained from powder samples on a Coderg T 800 Raman spectrometer (90” scattering geometry) using an argon ion laser (488 or 514.5 pm). INFRAREDAND
RAMAN SPECTRA
The i.r. and Raman spectra of some antimonates and tantalates have been published by HUSSON et al. [2]. The ir. data are in good agreement with our results, but in the Raman spectra there are differences concerning the frequencies of the vibrations and the number of observed Raman lines. Therefore we present our results on the Raman spectra of the antimonates and tantalates (see Figs. 2 and 3). Figures 4 and 5 show the i.r. and Raman spectra of some tellurates. The very poor Raman spectra of Cr,TeO, and Fe2Te06 are due to the dark colour of the samples. Perhaps better results could be obtained by using a red excitation line. [pm] of the investigated
trirutiles Tellurates
Tantalates
a0
c
o
@3Ta&j
A12Te06
444.7(l)
870.9(l)
NiSb206
NiTa206
Ga2Te06
454.6(l)
896.9(l)
CoSb206
CoTa206
Cr2Te06
454.7(l)
901.4(l)
FeSb206
Fe2Te06
460.6(l)
909.6(l)
ZnSb206
Mn2Te06
460.7(3)
911.9(9)
Wb206
487
H. HAEUSELER
488
According to the group theoretical analysis[l] there are for the trirutile-lattice at wavevector k = 0 12 i.r. active and 16 Raman active vibrations, all of which cannot be observed in the spectra. Especially the Raman spectra are not complete in most cases. For the interpretation of the spectra we have to consider two cases: (i) the antimonates can be regarded as to be built from units containing two Sb06 octahedra sharing an edge. These Sb,O,,units are linked by common vertices. The twovalent metal atoms occupy the resulting octahedral holes. The same description is possible for the tantalates. (ii) The tellurates and tungstate, on the other hand-sometimes referred to as inverse trirutiles-contain isolated TeO, and W06 octahedra, respectively. According to the normal coordinate calculations by HUSSON et a/.[21 the spectra of the tantalates and antimonates are dominated by the vibrations of the TatOlo and Sb20,, units, respectively. The participation of the two-valent metal atoms is very small. Only two i.r. active vibrations seem to be mainly vibrations of the M’*06 octahedron. These results cannot be transferred to the tellurates where tellurium occupies lhe same site as the two-valent metal atoms in the antimonates since there must be significant changes in the force constants and therefore in the assignment of the vibrations. In these compounds the high frequency absorptions should be due to the isolated Te06octahedra. Table 2 gives the correlation between the symmetries of the vibrations of a free TeO,octahedron to TeO,-octahedra under site group and unit cell group symmetry, respectively.
Fig. 1. Unit cell of GazTe06. 1,2 = Te; 3-6 = Ga; 7-18 = 0. The numeration of the atoms corresponds to Table 2.
SYMMETRYCOORDINATES
The ternary oxides of trirutile-type crystallize tetragonal (space group P4Jmnm-Dg) with two formula units per unit cell. The structure can be regarded as a superstructure of rutil type with an ordered distribution of the metal atoms on the titanium sites resulting in a tripling of the c-axis (Fig. 1). There are 18 atoms in the primitive cell resulting in a total of 51 vibrational modes. These modes have the irreducible representation [l] I = 4A,, +2A2, + 2B,, + 4B2, + 6E, + A,, + 4A2, + 5B,, + Bzu + 8E,,. The vibrations of species A,,, B,,, Bzg and E, are Raman-active, the modes with symmetries Azu and E. are i.r.-active. Based on Cartesian coordinates we have deduced Cartesian symmetry coordinates for all vibrations of the trirutile-lattice (see Table 3). From the symmetry coordinates one can see that the divalent metals in the tantalates and antimonates and the tellurium or tungsten in the tellurates and tungstate does not take part in all the Raman-active vibrations.
11
I
200
Fig.
2. Raman
I
400
I
I
600
I1
I
I
800
cm-’
spectra of some antimonates trirutile-type structure.
with
Infrared and Raman spectra and normal coordinate calculations
489
.5 b
-8
-B
-H -8 3s
8
-8 ‘E
I-
H. HAEUSELER
490
Table 2. Correlation diagram for the vibrations of the Te06octahedron under site group and unit cell group symmetry ibration
free octahedron
site group
“2
_-
/g------_
Eg ------I
A
yA1g B29
/
*29
Y
*1!3
Big-----A__ *
Ag-----B O5
-
FORCE FIELD AND FORCE CONSTANT CALCULATIONS
FOR Gs,TeO,
Following WILSON’S GF matrix method [9] extended for the treatment of lattice vibrations by SHIMANOUCHI et a/.[101 we have chosen a modified valence force field with 12 force constants: two Te-0 valence force constants j, and jZ corresponding to the two different Te-0 distances in the TeOs-octahedra, 3 Ga-0 valence force constants j3, j., and f5 corresponding to the various Ga-0 distances in the Ga,Olo units of the trirutile structure. For the interpretation of the absorptions especially in the long wavelength region we need furthermore some angle bending coordinates in the Te06 octahedron (j6, j,, j8) and in the GazOlo unit cfg, f~o, jr,, jr& For the number of the corresponding internal coordinates in the primitive cell and the interatomic distances and angles between the concerned atoms see Table 4. Since the Raman spectrum of Ga,TeO, is not complete and we could not exactly assign the Raman lines to the different Raman-active species we decided to do the force-constant calculations on the basis of the 12 i.r. frequencies only. Therefore we restricted for mathematical reasons our force field such that we used the following relations between the force constants: j, = j2, j3 = jd = j5, f6 = f, = f8 and jg = jlO. This means that we
unit cell group D4h
D2h
Oh
B29 -._ B3g 1
29 2Eg
used a set of 6 force constants for the interpretation of the vibrational spectra. Force constant calculations were carried out with the CDC Cyber 76 of the RRZ Cologne using a computer program the program LSMX by based on SHIMANOUCHI[l 11. The agreement between observed and calculated frequencies was checked by the function h=
c 2
(vci -
I.
~oi)*
n
The obtained values for the force constants are given in Table 4. The observed and calculated i.r. frequencies are presented in Table 5 along with the observed and calculated Raman frequencies, the assignment of the modes, and the potential energy distribution for the force constants.
DISCUSSION
For the obtained set of force constants (see Table 4) there is relatively good agreement between the observed and calculated frequencies (see Table 5) of the i.r.-active vibrations. The differences are within 15%. This seems to be good in consideration ot &e strong restrictions placed
Infrared and Raman spectra and normal coordinate calculations
Table 3. Symmetry coordinates
Alg:
S1
=
l
2
(2
3
-
(x, + y, -
s3
(-xl0
= :
+‘16 1 s4 = 2fi
(_Zll
Y8
xg +
-
Yg
+ x10
-
Y*(J)
+ y16 - x17 - Y17 - “18 + y18) + 212 - Z13 + ‘14
- ‘15
- ‘16
- Yll
- ‘17
- x12 - Y12 + Xl3 + Y13 + X14 + Y14 -95
- Y16 - ‘17
+ y17 + ‘18
s
(x7 + Y7 - X8 - Y8 + x9 - Yg - x10 - YlO)
slo= 1 $1 2-P Sll’
;
+ x12 - Y12 - x13 + Y13 - x14 + Y14 - X15 - Y15
+ y16 - ‘17
- Y17 + ‘18
- 212 + 213 - 94
- ‘15
(x3 - x4 - x5 + X6)
s13= ;
(z7 - Z8 + zg - 210)
sl4=2-h
h
S15’&kYll
- 92
s1*
+ ’ 13 - ‘14
- ‘15
- y18) - ‘16
+ ‘17
=;
+ ‘18)
(Y, - Y4 - Y5 - Y6)
- ‘16
+ ‘17
+ ‘18)
+ Y12 - Y13 - Y14 - Y15 - Y16 + Y17 + y18)
s16=2Lfl (‘11
+ z12 - 213 - z14 - z15 + ‘16 S18 = g
517 ‘8 l
(Zl + z2)
S19 = $
(2,
520 = a1
(x I* - Y11 - x12 + Y12 - 93 -‘16
-1 s kll 21 -27T 522 =h
+ Y15
- y18
(23 - z4 - 25 - Z6)
(x4 - Yll
- ‘18)
+ YlO)
s7 = $ =1 2fl
compounds
+ Yll - x12 + Y12 + x13 - Y13 + x14 - Y14 - x15 + Y15
(-x*1
+‘16
E’ ”
26)
-
S6 = :
sg = :
A2”
-
(x7 - Y, - x8 + Y8 - ‘9 - Yg + ‘10
8
E : g
X8
55 = ’ nff
+‘16 829 :
+ 15
s* = !
2lF
81g:
24
for the vibrations of trirutile-type
491
- ‘17
(23 + 24 + 25 + z6)
+ 28 + zg + ZlO)
- Y16 - ‘17
- Y17 + ‘18
+ Y13 + x14 - Y14 + ?5
+ z12 + z13 + z14 + z15 + ‘16
+ ‘17
‘23
=a l
(Yl - Y2)
(x 3 t x4 + x 5 + ‘6)
‘25
=3
(Y,
l = ;T
‘26
=i
‘28
=2-$(xl1
(x7 + X8 + xg +qo)
+ Xl2 + x13 + xl4
s2g =2Lfl C-Y11 -Yl2 530 =2Lfl(z11
s2, = $
+ Y15
+ y18)
(Xl + x2)
‘24
+ ‘18
+ ‘18)
+ Y4 - Y5 - Y6)
(Y, + y8 - Yg - YIOI
+ x15 + ‘16
+ ‘17
+ ‘18)
- Y13 - Y14 + Y15 + Y16 + Y17 + y18)
- 212 - z13 - 214 + 215 - ‘16
- ‘17
- ‘18)
*For species EBand EMonly one component of the two degenerate coordinates is given. The numeration corresponds to Fig. 1.
H.
492 Table 4. Internal coordinates,
,
internal
force constants, and correspondina interatomic distances and angles _ -
No of internal coordinates
coordinate
Te-0
4
Te-0
8
Ga-0
8
Ga-0
8
Ga-0
8
0-Te-0
16
0-Te-0
4
0-Te-0
4
0-Ga-0
16
0-Ga-0
16
HAELJSELER
force
interatomic
constant
or angle
[mdyn/R]
f1
distance
[I
[degrees]
1.935
3.10
1.921
fZ
1.963
f3
1.967
1.12
f4
1.976
f5
90.00
f6 0.73
f7
80.9’ 99.10
f8 f9
89.4’
0.05
90.6’
f10
0-Ga-0
8
fll
0.19
100.20
0-Ga-0
4
f12
0.47
78.2’
8
on the force field, i.e. the use of only six independent force constants. The value of the Te-0 stretching force constant of 3.1 mdyn A-’ is comparable to the values obtained for the Te-0 bond in some other tellurates with different structures. LENTZ[12] gives a
value of 2.46mdyn A-’ for the Te-0 bond in a tellurate with elpasolite structure, FADINI et al. [ 131 find a mean value of 3.7 mdyn A-’ for some perovskite tellurates and BARAN et al. [14] have calculated the Te-0 force constant to be 3.45 mdyn A-’ in spine1 type compounds. The calculations by
Table 5. Observed and calculated frequencies [cm-‘], assignment, and potential energy distribution for the force constants of GalTe06 IR
Raman PEO
0
Qc
780
771
742 701
species
PED
f1/2
f3/4/5
f6/7/8
Aeu
69
9
3
2
745
Eu
67
19
7
715
Eu
67
20
13
649
642
A2”
-
45
602
584
Eu
22
40
560
578
A2”
1
542
489
Eu
1
373
422
E,
1
5
328
334
At”
8
45
0
f9/10
fll
f12
2
15
-
7
-
-
-
-
49
1
4
1
34
4
-
-
45
50
1
3
-
7
85
5
2
-
86
7
I-
21
5
-
21
20
2
-
‘0
gc species
f1/2
f3/4/5
f9/10
fll
f12
22
-
4
13
26
23
-
4
13
34
30
28
2
3
3
Alg
37
29
26
1
4
3
E g
21
22
49
2
6
-
664
82g
65
19
9
663
Alg
63
19
11
1
1
5
648
Eg
50
25
23
1
1
-
528.
557
Elg
-
-
92
8
-
-
408
464
E g
10
84
I
4
l-
14
14
2
-
750
82g
35
26
749
Alg
34
699
699
82g
690
695 673
791
650
608
f6/7/8
.
115
279
277
E,
8
47
23
249
257
Eu
16
45
4
11
24
-
3C4
290
Eg
1
70
142
121
Eu
2
46
9
40
3
-
298
264
Alg
14
48
7
13
2
16
251
B2g
20
48
11
4
3
14
230
Eg
2
44
4
16
34
-
150
Eg
9
25
1
37
28
-
68
Big
-
-
6
94
-
-
201 140
493
Infrared and Raman spectra and normal coordinate calculations FADINI et al.[13] and BARAN et al.[l41 are based on the assumption of fully isolated TeO, octahedra neglecting all couplings to other parts of the structures. Therefore their values for the TeO stretching force constant may be falsified a little bit. But in conclusion one can say, that the Te-0 stretching force constant is only slightly dependent on the structure,and lies, at least in tellurates with isolated Te06 octahedra, near the value 3.0 mydn k’ that is calculated for a covalent single bond by SIEBERT’Sproduct rule [ 151. As can be seen from the potential energy distribution for the force constants (see Table 5) the three shortwaved modes in the i.r. spectrum (see also Fig. 6) are mainly vibrations of the TeO,-octahedron. This is in accordance with the correlation diagram of Table 2 which predicts that the vj of the octahedron under unit cell group symmetry splits into three components: 1A2, and 2E,, vibrations.
A2o 771
A2u 334
The assignment of the three absorption maxima (see Table 5) obtained by the normal coordinate calculations corresponds with these predictions. The vibrations at 649, 602 and 560cm-’ show strong participation of the Ga-0 stretching constant and the 0-Te-0 angle bending force constant. This means that there is strong coupling of the bending vibration vq of the octahedron with some stretching vibrations in the Ga,OIO unit. Only the two modes at 542 and 373 cm-’ can be regarded as to be of nearly pure bending character. The remaining longwaved i.r.-active modes are more or less strong affected by the force constants in the Ga,O,, polyhedra with only small participation of the Te06 group. The agreement between the observed and calculated frequencies of the Raman-active vibrations is not so good as for the i.r.-active vibrations and the assignment given in Table 5 is only tentative.
Eu 745
Eu 715
A2,,
EU 489
578
EU 277
Eu
257
A2u 642
E,,
422
Eu
121
Fig. 6. Vibrational modes and calculated wavenumbers [cm-‘] of GazTe06 in the i.r.-active species Azu and E..
SAA
Vol. 37A, No. 1-C
H. HAEUSELER
Al9
749
f3zg 664
Eg 464 Fig. 7. Vibrational
Al9
695
Alg
Big
68
B2g
B2g
Eg
251
290
663
750
Alg
BP9
264
699
Eg
673
Eg
648
Eg
230
Eg
150
modes and calculated wavenumbers [cm-‘] of GazTeOc in the Raman-active species A,,, B,,, Bzg and E8
As can be seen from the potential energy distribution (Table 5) the modes of species A,, and Bzr are (see also Fig. 7) mainly vibrations of the TeOs octahedra with mixed stretching and bending character. The small differences between the calculated values of the Al, and Big vibrations (see Table 5) show that correlation splitting for these vibrations is expected to be small. This may be an effect of the restricted force field which includes
only nearest neighbour interactions but on the other hand this could be the cause that the number of observed Raman lines is not in agreement with group theoretical predictions.
REFERENCES [l] R. FRANCK, C. ROCCHICCIOLI-DELTCHEFF and J. GUILLERMET,Spectrochim. Acta 3OA, 1-14 (1974).
Infrared and Raman spectra and normal coordinate calculations [2] E. HUSSON,Y. REPELIN, H. BRUSSETand A. CEREZ, Spectrochim. Acta 35A, 1177-1187 (1979). [3] G. M. CLARK and W. P. DOYLE, Spectrochim. Acta 22, 1441-1447 (1966). [4] G. BAYER, Ber. Dtsch. Keram. Ges. 39, 535-554 (1962). [5] A. BYSTR~M, B. H~K and B. MASON, Arkio Kemi, Miner. Geol. 15B(4), l-8 (1941). [6] F. HUND, Naturwissenschaften 58, 323 (1971). [7] L. DEGUELDRE, Y. GOBILLON, L. BURGEOIS, U.S. 3,736,269; CA 19: P 55561. [8] T. BIRCHALL, J. Solid State Chem. 27, 293-298 (1979). [9] E. B. WILSON, J. C. DECIUS and P. C. CROSS, Molecular Vibrations. McGraw-Hill, New York, Toronto, London (1955).
495
[lo] T. SHIMANOUCHI,M. TSUBOI and T. MIYAZAWA, J. them. Phys. 35, 1597-1612 (1961). 1111 . _ T. SHIMANOUCHI.Computer Programs for IiIormal Coordinate Treatment- of Polyatomic- Molecules, Tokyo (1968). [12] A. LENTZ, J. Phys. Chem. Solids 35,827-832 (1974). 1131 _ _ A. FADINI. I. Joos. S. KEMMLER-SACK.G. RAUSER. H.-J. ROTHER,E. S~HILLINGER,H.-J. SCHIITENHEL~ and U. TREIBER, Z. anorg. allg. Chem. 439, 35-47 (1978). [14] E. J. BARAN and I. L. BOITO, Z. anorg. aHg. Chem. 463, 185-192 (1980). 1151 H. SIEBERT, Anwendungen der Schwingungsspektroskopie in der Anorganischen Chemie. Springer, Berlin, Heidelberg, New York (1966).