Synthesis and modulated crystal structure of KBaNbS4

Article abstract of DOI:10.1002/zaac.200500255

Single crystals of KBaNbS₄ have been prepared by the reaction of Nb with an in situ formed melt of K₂S₃, BaS, and S at 500°C. Satellite reflections observed in X-ray diffraction experiments of these crystals indicate the presence of a one-dimensional lattice distortion. The modulated structure has been solved and refined from X-ray data using the superspace group approach. KBaNbS₄ can be described in the (3 + 1)-dimensional superspace group Pnma(α00)0s0 with lattice parameters a = 9.187(1), b = 7.001(1), and c = 12.494(1)A and a modulation vector q = (0, 0.629(1), 0). In the structure the NbS₄ tetrahedra are stacked along the a axis and show a slight tilting against each other. The K⁺ and Ba²⁺ ions follow this tilting, both are slightly shifted from their positions in the average structure. The modulation does not lead to a significant change in the coordination spheres of the metal atoms. The small effects of the modulation correspond to the relatively weak intensities of the satellite reflections. Results of temperature dependent X-ray investigations indicate that K⁺ librates at higher temperatures and the surrounding S²- anions follow this motion. With decreasing temperature the libration of K⁺ is reduced and the coordination geometry freezes under formation of an incommensurate modulation. The heavier Ba and Nb atoms are also affected by positional modulation of the substructure and accommodate to their environment.

Full text of DOI:10.1002/zaac.200500255

Synthesis and Modulated Crystal Structure of KBaNbS4
a
b
a,
Yuandong Wu , Thomas Doert , and Wolfgang Bensch *
a
Kiel, Institut für Anorganische Chemie der Christian-Albrechts Universität
Dresden, Institut für Anorganische Chemie der Technische Universität Dresden
b
Received June 2nd, 2005.
Abstract. Single crystals of KBaNbS
reaction of Nb with an in situ formed melt of K
00 °C. Satellite reflections observed in X-ray diffraction experi-
ments of these crystals indicate the presence of a one-dimensional
lattice distortion. The modulated structure has been solved and
refined from X-ray data using the superspace group approach.
4
have been prepared by the
to a significant change in the coordination spheres of the metal
atoms. The small effects of the modulation correspond to the relati-
vely weak intensities of the satellite reflections. Results of tempera-
2 3
S
, BaS, and S at
5
ϩ
ture dependent X-ray investigations indicate that K librates at hig-
2
Ϫ
her temperatures and the surrounding S anions follow this mo-
ϩ
tion. With decreasing temperature the libration of K is reduced
KBaNbS
4
can be described in the (3 ϩ 1)-dimensional superspace
and the coordination geometry freezes under formation of an in-
commensurate modulation. The heavier Ba and Nb atoms are also
affected by positional modulation of the substructure and accom-
modate to their environment.
group Pnma(α00)0s0 with lattice parameters a ϭ 9.187(1), b ϭ
˚
7.001(1), and c ϭ 12.494(1) A and a modulation vector q ϭ (0,
4
0.629(1), 0). In the structure the NbS tetrahedra are stacked along
ϩ
the a axis and show a slight tilting against each other. The K and
2ϩ
Ba ions follow this tilting, both are slightly shifted from their
positions in the average structure. The modulation does not lead
Keywords: Niobium; Potassium; Barium; Modulated Crystal Struc-
ture; Flux reaction
Introduction
atoms and the other by eight or ten Q atoms. The above
mentioned compounds were prepared either by heating
stoichiometric amounts of the corresponding elements at
elevated temperatures or by the reaction between the re-
spective metal M with the elemental chalcogenides in alkali
metal polychalkogenide fluxes (reactive flux method).
As a part of the expanded chemistry of the reactive flux
The alkali tetrachalcogenometallates A MQ (A ϭ Na, K,
Rb, Cs; M ϭ V, Nb, Ta; Q ϭ S, Se) [1Ϫ12] and A MQ4
3
4
2
(
A ϭ NH , K, Rb, Cs; M ϭ Mo, W; Q ϭ S, Se) [8, 13Ϫ18]
4
3
Ϫ
are characterized by discrete tetrahedral MQ4 anions and
alkali metal cations. Since the crystal structure of K VS4
was reported [4, 5], 14 members of the A MQ family have
been prepared whose structures were determined from
single crystal X-ray or neutron diffraction powder studies.
Among these compounds Na VS [1] crystallizes in the tet-
ragonal system and Na NbS [2] as well as Na TaS [2, 3]
adopt F centered orthorhombic cells. The K, Rb, and Cs
compounds [4Ϫ12] crystallize in space group Pnma (stand-
ard setting) and are of the K VS structure type. The anions
3
3
4
method,
we
recently
reported
the
compound
K Ba (Nb S ) [19]. The occurrence of statistically distrib-
4
2
2 11 2
uted Ba2 /K ions leads to the formation of two distinct
ϩ
ϩ
3
4
4Ϫ
[
Nb S ] anions. These two anions show a very similar
2 11
3
4
3
4
topology but they are surrounded by a different number of
2ϩ
ϩ
Ba and K cations, respectively. In continuing experi-
ments we tried to prepare quaternary group 1/group 2 ni-
obium chalcogenides based on A MS . It is of special inter-
3
4
3
4
have crystallographically imposed m symmetry with the me-
tal atom located on a special position. The two crystallo-
graphically independent alkali metal cations in A MQ4
est whether such compounds can be prepared which are still
based on [NbS4]3 units and whether Ba and K cations
occupy statistically the same position as observed in
K Ba (Nb S ) . Because both cations exhibit approxi-
Ϫ
2ϩ
ϩ
3
(
A ϭ K, Rb) are coordinated by seven Q atoms of four and
3
Ϫ
4
2
2 11 2
six MQ4 ions, respectively. In the cesium compound one
of the Cs ions is linked to five and the second to seven
mately the same ionic radius, the influence of the differing
charge can be studied in particular. Here we report the syn-
thesis and structural characterization of the group 1/group
ϩ
3
Ϫ
˚
Se atoms each of four MSe4 ions (A···Q cut-off of 4 A).
Without exception, all members of the A MQ family crys-
tallize in the orthorhombic space group Pnma and are iso-
2
4
2
niobium chalcogenide KBaNbS4.
structural. The structure contains discrete tetrahedral
2
Ϫ
ϩ
MQ4 anions of symmetry m, separated by A cations.
ϩ
Results and Discussion
One of the two unique A cations is surrounded by nine Q
Crystal structures
*
Prof. Dr. W. Bensch
The average structure of KBaNbS is depicted in Figure 1
4
Institut für Anorganische Chemie der Universität Kiel
Olshausenstr. 40
D-24098 Kiel
Fax: ϩ49 (0)431/880 Ϫ1520
e-Mail: wbensch@ac.uni-kiel.de
as a projection along a. The structure consists of discrete
[
[
NbS4]3 tetrahedra separated by K and Ba cations. The
Ϫ
ϩ
2ϩ
3Ϫ
NbS4]
tetrahedron is somewhat distorted and the Nb-S
˚
˚
˚
distances are 2.252(3) A (2ϫ), 2.273(1) A, and 2.274(1) A.
Z. Anorg. Allg. Chem. 2005, 631, 3019Ϫ3024
DOI: 10.1002/zaac.200500255
© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim
3019

Y. Wu, T. Doert, W. Bensch
˚
ϩ
With a cut-off of 4.0 A for K-S and Ba-S bonds K occu-
pies a void with ninefold coordination of S atoms with K-
along a, b and c are allowed. We chose the Fourier section
x3Ϫx4 to visualize the displacement of this atom since its
maximum dislocation is observed along x3.
˚
2ϩ
S distances between 3.194(2) and 3.987(4) A. Ba is also
coordinated by nine S atoms with distances between
As can be estimated from the comparatively small values
of the Fourier coefficients of modulation waves (Table 1),
the overall results of the modulation are quite minute at
˚
3.212(1) and 3.701(4) A (Fig. 2 and 3). All distances are
reasonable and can be compared to those found in K NbS4
3
[
6] and BaNbS [20].
T ϭ 180 K. Fig. 5 shows a NbS tetrahedron in the average
3
4
The results of the modulation for the individual atoms
can best be visualized in the Fourier sections (Fig. 4). These
figures display the electron density distribution (F ) around
o
the respective atom positions along the modulation direc-
tion x4. As can be seen from the values in Table 1, the
magnitudes of displacement of the individual atoms are qu-
ite different in different directions of space. The site sym-
metry of the atomic positions occupied in the space group
Pnma(α00)0s0 induces certain restrictions for the modu-
lation waves. For K, Ba, Nb, S(1) and S(3), all located on
Wyckoff sites 4c (site symmetry .m.), no dislocation along
the a- and c-axis are possible. For these atoms, the Fourier
sections x2Ϫx4 are therefore displayed. Only for S(2) on
Wyckoff site 8d (site symmetry 1), effects of the modulation
ϩ
Fig. 3 Sulphur coordination environment of Ba2 cation in the av-
erage structure of KBaNbS
4
Fig. 1 Crystal structure of the average structure of KBaNbS
4
down
[100]; the unit cell is indicated.
Fig. 4 Fourier sections (F
o
) calculated around the positions of K
(
(
top left), Ba (top center), Nb (top right), S(1) (bottom left), S(2)
bottom center), and S(3) (bottom right); the central lines display
the calculated atomic positions; the black lines indicate areas of
equivalent electron density (in steps of 10 % of the observed maxi-
mum electron density)
ϩ
Fig. 2 Sulphur coordination environment of K cation in the aver-
age structure of KBaNbS
4
3020
© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim
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Z. Anorg. Allg. Chem. 2005, 631, 3019Ϫ3024

Synthesis and Modulated Crystal Structure of KBaNbS
4
structure (left) and in the modulated structure (right), both
viewed along b. Only a weak tilting is observed in the
modulated structure. Fig. 6 shows a larger section of the
erage structure. The small effects of the modulation corre-
spond to the weak intensities of the satellite reflections.
Only 256 first order satellites (out of 1488 measured) have
intensities larger than I Ն 3σ(I), all higher order satellites
have lower intensities than 3σ(I) or are close to this value.
The changes in the inter-atomic distances depending on
the internal coordinate t are displayed in Fig. 7, with t being
the additional coordinate for the phase of the modulation
function for (3ϩ1)-dimensional structures. The modulation
obviously affects the NbϪS distances less than the respect-
ive KϪS and BaϪS distances. The NbϪS bonds change
only slightly with t and all four distances are modulated to
a similar extend. The maximum deviations from the average
modulated structure of KBaNbS down [100]. As a result
4
of the modulation, the NbS tetrahedra stacked along a do
4
not superimpose exactly. Instead, a slight tilting against
ϩ
2ϩ
each other is visible. K and Ba ions follow this tilting,
and both are slightly shifted from their positions in the av-
4
Table 1 Fourier coefficients (ϫ 10 ) of the site modulation function
S ϭ sine-, C ϭ cosine-term in x, y, and z direction, respectively)
(
atom
Nb
x
0
0
0
0
0
0
0
y
z
0
0
0
0
0
0
0
S
C
S
C
S
C
S
C
S
C
S
C
Ϫ2(2)
46(2)
131(1)
22(2)
120(5)
Ϫ12(5)
339(5)
Ϫ86(7)
Ϫ113(3)
51(4)
˚
˚
bond lengths are 0.007 A for NbϪS(1), 0.01 A for
˚
Ba
NbϪS(2), and 0.004 A for NbϪS(3). The situation is differ-
ent regarding the KϪS and BaϪS distances. In the Ba coor-
dination, two bonds (both between Ba and S(3)) alter sig-
nificantly whereas the other seven distances are smoothly
modulated. The maximum deviations of the two BaϪS(3)
K
S(1)
S(2)
S(3)
0
0
56(4)
Ϫ98(4)
0
0
150(3)
Ϫ55(3)
0
0
˚ ˚
bond lengths are 0.281 A and 0.283 A. The KS polyhedron
9
Ϫ289(5)
Ϫ30(8)
shows an opposite picture: three distances remain nearly
unaffected, the other six are strongly modulated. The maxi-
˚
mum deviation of the KϪS distance spectrum is 0.269 A
˚
4
Table 2 Selected interatomic distances for KBaNbS in A
for one KϪS(2) contact.
At T ϭ 200 K, the results of the modulation are even
smaller. The refined Fourier coefficients of the site modu-
lation functions result in about 70 % of the numerical values
average
3.933(1)
3.730(1)
2.274(1)
2.252(3)
2.252(3)
2.273(1)
3.278(1)
3.212(1)
3.224(4)
3.224(4)
3.237(3)
3.237(3)
3.256(1)
3.701(4)
3.696(4)
3.765(2)
3.536(5)
3.535(5)
3.555(4)
3.572(4)
3.555(4)
3.571(4)
3.987(4)
3.985(4)
3.194(2)
3.686(4)
3.900(4)
3.686(4)
3.899(4)
3.696(4)
3.697(4)
3.735(2)
3.399(4)
3.631(4)
3.714(4)
3.949(4)
min.
max.
NbϪBai
NbϪK
NbϪS(1)
NbϪS(2)
NbϪS(2)
NbϪS(3)
BaϪS(1)
3.932(1)
3.730(1)
2.267(1)
2.243(3)
2.243(3)
2.269(1)
3.275(1)
3.209(1)
3.218(4)
3.218(4)
3.221(3)
3.221(3)
3.249(1)
3.420(3)
3.420(3)
3.761(2)
3.359(5)
3.359(5)
3.435(4)
3.315(4)
3.435(4)
3.315(4)
3.718(4)
3.718(4)
3.191(2)
3.672(5)
3.794(4)
3.672(5)
3.794(4)
3.648(5)
3.648(5)
3.724(2)
3.386(4)
3.619(4)
3.693(4)
3.806(5)
3.934(1)
3.731(1)
2.280(1)
2.262(3)
2.262(3)
2.276(1)
3.282(1)
3.215(1)
3.236(3)
3.236(3)
3.253(3)
3.253(3)
3.263(1)
3.979(3)
3.979(3)
3.769(2)
3.713(5)
3.713(5)
3.672(4)
3.828(4)
3.672(4)
3.828(4)
4.254(4)
4.254(4)
3.198(2)
3.705(4)
4.001(4)
3.705(4)
4.001(4)
3.750(4)
3.750(4)
3.746(2)
3.412(4)
3.643(4)
3.734(4)
4.090(5)
ii
iii
iv
BaϪS(1)
BaϪS(2)
BaϪS(2)v
vi
BaϪS(2)
BaϪS(2)
BaϪS(3)
BaϪS(3)
BaϪS(3)
KϪS(1)
vii
iii
vi
viii
iv
KϪS(1)
KϪS(1)
KϪS(2)
KϪS(2)
ix
Fig. 5 One NbS -tetrahedron in the average structure (left) and in
4
the modulated structure (right).
iv
ii
KϪS(2)v
KϪS(2)
vi
KϪS(2)x
KϪS(2)
xi
KϪS(3)
S(1)ϪS(2)
S(1)ϪS(2)
S(1)ϪS(2)
iv
ii
S(1)ϪS(2)v
vi
S(1)ϪS(2)
S(1)ϪS(2)
S(1)ϪS(3)
S(2)ϪS(2)
S(2)ϪS(2)
S(2)ϪS(3)
S(2)ϪS(3)
vii
xii
ii
vi
symmetry codes:
Ϫ1/2Ϫx,Ϫy,3/2ϩz
iv 1Ϫx,Ϫy,1Ϫz
i
ii Ϫx,1/2ϩy,Ϫz
1Ϫx,1/2ϩy,1Ϫz
viii 1/2Ϫx,1Ϫy,1/2ϩz
xi 1Ϫx,Ϫy,Ϫz
iii 1/2Ϫx,Ϫy,3/2ϩz
vi 1/2Ϫx,Ϫy,1/2ϩz
ix 1Ϫx,1Ϫy,1Ϫz
xii Ϫx,Ϫ1/2ϩy,Ϫz
v
Fig. 6 Crystal structure of the modulated structure of KBaNbS
4
vii 1/2Ϫx,1/2ϩy,1ϩz
along [100]; the tilting of the NbS
clearly visible.
4
-tetrahedra against each other is
x
1/2Ϫx,1/2ϩy,1/2ϩz
Z. Anorg. Allg. Chem. 2005, 631, 3019Ϫ3024
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© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim
3021

Y. Wu, T. Doert, W. Bensch
for the respective Fourier coefficients at T ϭ 180 K. Only a
puted for T ϭ 180 K and no difference is observed compar-
ing both structures. At temperatures above at least 250 K,
no satellites are visible in the diffraction image and no
superspace refinement is possible. However, the three-di-
mensional structure model refined with the respective data
sets yields some large anisotropic displacement parameters,
especially for potassium and the sulphur atoms. This indi-
cates that the effects of the modulation are more and more
covered by the thermal motion of the respective atoms at
higher temperatures, but the modulation is still present in
the structure.
tiny distortion of the NbS tetrahedra is visible in the struc-
4
ture in this case. At T ϭ 150 K, the Fourier coefficients of
the modulation functions are almost equal to those com-
ϩ
2ϩ
As no evidence for a K /Ba
positional disorder is
found, the most reasonable explanation for the modulation
lies in the different sizes of the coordination spheres for
these two atoms. At 180 K, the average BaϪS distance is
˚
about 3.34 A (cf. table 5) which corresponds to the sum of
˚
2ϩ
the ionic radii of 3.31 A for Ba (with coordination num-
ber 9) and S2 [19]. But the average KϪS distance is ap-
Ϫ
˚
proximately 3.63 A and considerably larger than the sum of
˚
ϩ
2Ϫ
the ionic radii of 3.39 A for K (CN 9) and S [19]. The
same observation can be made at different temperatures.
The larger anisotropic displacement parameters at higher
ϩ
temperatures for K indicate a thermal libration of this rel-
atively light atom in the large void with the consequence
that the coordinating S2 anions follow this motion. Upon
cooling, the libration is reduced and the coordination ge-
ometry freezes under formation of an incommensurate
modulation. With this distortion of the sulphur substruc-
ture, the heavier Ba and Nb atoms are also affected by the
positional modulation and they have to adapt to their sur-
roundings.
Ϫ
Our efforts to prepare and characterize new thioniobates
within the quaternary phase system K/Ba/Nb/S have led to
the new compounds K Ba (Nb S ) [20] and KBaNbS .
4
2
2
11 2
4
These promising results are the basis for further investi-
gations which will aim at the incorporation of group two
metal cations as these might result in new materials. The
different occupations of the cation sites in the structures
encourage the determination of their physical properties; es-
pecial the structureϪproperty relationship is of special
interest in the context.
Experimental
Syntheses
The compound KBaNbS
, BaS, Nb, and S in a 1:1:1:4 molar ratio (Nb, 99.99 %, Fluka;
BaS, 99.99 % purity, Alfa; S, 99.99 %, Heraeus). K was synthe-
sized by the reaction of stoichiometric amounts of the elements (K
99 %, Chempur) in liquid ammonia under argon atmosphere.
The reaction mixture was thoroughly mixed in a N -filled glove
4
was prepared by reacting a mixture of
2 3
K S
2 3
S
>
2
Ϫ3
box and loaded into glass ampoules. After evacuation to 10 mbar
the ampoule was flame-sealed and placed in a computer-controlled
furnace. The mixture was heated to 500 °C at a rate of 0.5 °C/min.
This temperature was kept for 6 days before the sample was cooled
down to 100 °C at a rate of 2 °C h followed by cooling to room
temperature within 10 h. The product was washed with dry DMF
˚
Fig. 7 Modulation of the interatomic distances (A) along t, top:
NbϪS-distances (the distances of the average structure are given as
dashed lines for comparison), centre: KϪS-distances, bottom:
BaϪS-distances (distances of the average structure are omitted for
the sake of clarity).
Ϫ1
3022
© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim
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Z. Anorg. Allg. Chem. 2005, 631, 3019Ϫ3024

Synthesis and Modulated Crystal Structure of KBaNbS
4
and acetone yielding transparent yellow needles of the title com-
pound (yield: ϳ40 % based on Nb). The compound is very moist-
ure sensitive. EDX analyses were performed on freshly cleaved faces
of ten crystals. The overall composition K1.06(5)Ba1.00(5)Nb1.09(6)
software package [21] and refined with the program NADA [22] for
these data sets. The modulation vector has been found to be vir-
tually constant (α ϭ 0.631 ± 0.003) over this temperature range.
The intensities of the satellites increase slightly with decreasing
temperature indicating that the effects of the modulation become
stronger upon cooling. Because no principally new features of the
modulated structure occur at different temperatures, we present
only the structure model obtained from the data set measured at
180 K in detail. An empirical absorption correction has been ap-
plied to the data sets. The average and the modulated structures
were refined with the program JANA2000 [23]. Extinction effects
were corrected according to Becker and Coppens [24].
S3.95(6) was determined; no traces of any other elements were found.
Refinement of the occupancies of the K position and Ba position
during refinement of the average structure yielded values of 1.03(1)
and 0.99(1), respectively. Due to large correlation with some modu-
lation parameters, the occupancies were fixed at 1.00 for both K
and Ba positions during the refinement of the modulated structure.
Single crystal X-Ray diffraction
4
KBaNbS was found to crystallize in an orthorhombic unit cell
˚
˚
A crystal with dimensions given in Table 3 was investigated on
an Imaging Plate Diffractometer System (IPDS-1, STOE & Cie,
with dimensions a ϭ 9.187(1) A, b ϭ 7.001(1) A and c ϭ
˚
12.494(2) A at 180 K. The reflection conditions hk0, h ϭ 2n and
Darmstadt, Germany) with graphite monochromated Mo-K
α
radi-
0kl, k ϩ l ϭ 2n for the average structure are compatible with the
orthorhombic space groups Pnma (No. 62) and Pna21 (No. 33)
[25]. Additionally, weak satellite reflections were observed in the
diffraction pattern indicating the presence of an incommensurate
modulation along b. The satellites can be indexed with a modu-
lation vector q ϭ (0, 0.629(1), 0). The reflection conditions h0lm:
reflections only observed for m ϭ 2n and h00m: reflections only
observed for h ϩ m ϭ 2n point towards the centrosymmetric (3ϩ1)-
dimensional orthorhombic superspace group Pnma(a00)0s0 [26].
The respective superspace symmetry operations are given in Table
5.
˚
ation (λ ϭ 0.71073 A). Data collections were carried out tempera-
tures of 293, 250, 200, 180 and 150 K, respectively. Satellite reflec-
tions are visible in data sets recorded at T ϭ 200, 180 and 150 K.
The modulation vector has been determined with the IPDS
4
Table 3 Crystallographic and refinement data for KBaNbS .
empircal formula
KBaNbS
4
397.6 g molϪ1; 720
formula weight; F(000)
crystal dimensions
diffraktometer; radiation
crystal system
0.13 ϫ 0.10 ϫ 0.08
STOE IPDS-1, Mo Kα
orthorhombic
Structure solutions for the average structure were done in both pos-
superspace group
measuring temperature
structur refinement
Pnma(α00)0s0
sible orthorhombic space groups, Pnma and Pna2 . The metal
atoms were found by direct methods (SHELXS, [27]). The sulphur
positions could be located by subsequent inspection of the differ-
o c
ence Fourier map (F ϪF ) during structure refinements. The unit
cell dimensions and the initial atomic parameters of KBaNbS indi-
4
2 4
cated a close structural relationship to Rb WS [16], e. g. K and
Ba were found to occupy distinct sites, no indications for a mixed
occupation were observed. However, it was not possible to achieve
a satisfactory structure model including anisotropic displacement
parameters for all atoms in either of the two space groups in ques-
tion, several atoms were always found non-positive definite.
1
180 K
JANA2000 [23],
2
full matrix against F
˚
unit cell dimensions
a ϭ 9.187(1) A
˚
b ϭ 7.001(1) A
˚
3
c ϭ 12.494(1) A
˚
unit cell volume
modulation vector
calc. density; Z
absorption coefficient
absorption correction; Tmin; Tmax
measuring range
V ϭ 803.6(2) A
q ϭ (0, 0.629(1), 0)
Ϫ3
3.29 Mg m ; 4
Ϫ1
7.75 mm
empirical; 0.268; 0.383
Ϫ11 Յ h Յ 11;
Ϫ8 Յ k Յ 8;
Ϫ15 Յ l Յ 15;
Ϫ1 Յ m Յ 1;
Since no hints for an additional ordering pattern of K and Ba
atoms and no indications of a site occupancy wave were observed,
the incommensurate modulation appeared to be of the displacive
type. Therefore, the refinement of the modulated structure was
started by introducing harmonic displacive modulation waves for
the K, Ba and Nb atoms subsequently. Only first order satellites
were used for the refinements, since all higher order satellites have
2
.8 Յ θ Յ 26.9
measured reflections
classified as observed
independent reflections; observed
14804
with I > 3(I)
2384, 1029; Rintϭ 0.106
896; 773
main reflections; observed
st
1
order satellites; observed
1488; 256
restrictions / parameters
weighting scheme
Goodness-of-Fit
R-values
0 / 89
2
2
w ϭ 1/[σ (I)ϩ(0.0004(I )]
1.05
Table 5 Symmetry operations for superspace group Pnma(α00)0s0
R
1
; wR obs. reflections
2
; wR all reflections)
2
(R
1
main reflections and satellites
0.023, 0.047 (0.076, 0.054)
0.019, 0.044 (0.025, 0.045)
0.064, 0.126 (0.298, 0.216)
x1, x2, x3, x4
Ϫx1, Ϫx2, Ϫx3, Ϫx4
1
1
1
1
main reflections only
x1, /
2
Ϫx2, x3, /
2
ϩx4
Ϫx1, /
2
ϩx2, Ϫx3, /
2
Ϫx4
st
1
1
1
1
1
order satellites only
/
/
2
ϩx1, x2, /
2
Ϫx3, x4
/
/
2
Ϫx1, Ϫx2, /
2
ϩx3, Ϫx4
˚
Ϫ3
1
1
1
1
1
1
1
1
max. / min. difference Fourier
ϩ1.06 / Ϫ1.20 e A
2
ϩx1, /
2
Ϫx2, /
2
Ϫx3, /
2
ϩx4
2
2 2 2
Ϫx1, / ϩx2, / ϩx3, / Ϫx4
4
˚
2
4
Table 4 Atomic coordinates (ϫ 10 ) and displacement parameters (A ϫ 10 ) for KBaNbS
4
atom
Nb
Ba
site
4c
4c
4c
4c
8d
4c
x
y
z
U
31(1)
76(1)
209(3)
142(5)
171(4)
146(4)
eq
U
11
U
56(2)
157(1)
224(5)
315(11)
118(4)
321(9)
22
U
33
U
0
0
0
0
Ϫ14(3)
0
12
U
4(1)
Ϫ7(1)
Ϫ49(4)
Ϫ43(4)
106(6)
Ϫ17(4)
13
U
23
2311(1)
4788(1)
6370(1)
3096(2)
3203(1)
Ϫ158(2)
2500
2500
2500
2500
Ϫ83(1)
2500
4215(1)
8242(1)
4127(1)
5935(1)
3376(1)
4158(1)
15(2)
33(1)
60(6)
68(6)
129(6)
33(6)
21(2)
39(1)
342(6)
45(5)
266(8)
85(5)
0
0
0
0
K
S(1)
S(2)
S(3)
Ϫ113(4)
0
Z. Anorg. Allg. Chem. 2005, 631, 3019Ϫ3024
zaac.wiley-vch.de
© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim
3023

Y. Wu, T. Doert, W. Bensch
intensities close to or below the 3σ(I) criterion. The number of
harmonic modulation parameters was thus limited to one for the
modulation functions of all atoms. The refinement proceeded
smoothly and in the last steps, displacive modulation waves for the
S2 atoms and modulation functions for the displacement param-
eters of all atoms were introduced, too.
[10] B. Deng, J. A. Ibers, Acta Crystallogr. 2004, E60, i147.
[11] O. Krause, C. Näther, W. Bensch, Acta Crystallogr. 1999,
C55, 1197.
[12] H. Yun, C. R. Randall, J. A. Ibers, J. Solid State Chem. 1988,
76, 109.
[13] C. C. Raymond, P. K. Dorhout, S. M. Miller, Z. Kristallogr.
1
995, 210, 775.
Further information can be obtained from the Fachinformationsz-
entrum Karlsruhe, D-76344 Eggenstein-Leopoldshafen (fax:
[
14] J. Ellermeier, C. Näther, W. Bensch, Acta Crystallogr. 1999,
C55, 1748.
(ϩϩ49)7247-808-666 e-mail: crysdata@fiz.karlsruhe.de), on quot-
[
[
[
15] K. Sasv a` ri, Acta Crystallogr. 1963, 16, 719.
16] J.-Y Yao, J. A. Ibers, Acta Crystallogr. 2004, E60, i10.
17] D. Röhnert, C. Näther, W. Bensch, Acta Crystallogr. 1997,
C53, 165.
ing the depository numbers CSD 415335.
Acknowledgement. Financial support by the State of Schleswig-
Holstein is gratefully acknowledged.
[
[
18] A. Müller, B. Krebs, H. Beyer, Z. Naturforsch. 1968, 23b, 1537.
19] R. D. Shannon, C. T. Prewitt, Acta Crystallogr. 1969, B25,
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© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim
zaac.wiley-vch.de
Z. Anorg. Allg. Chem. 2005, 631, 3019Ϫ3024