Tl2S: Re-determination of crystal structure and stereochemical discussion

Article abstract of DOI:10.1006/jssc.2002.9711

The crystal structure of synthetic carlinite, Tl₂S, was redetermined by single crystal and powder X-ray diffraction methods. The cell parameters obtained from Rietveld refinement are a = 12.150(2) A, c = 18.190(4) A, V= 2325.5(7) A³. A single crystal data refinement proved Tl₂S crystallizing in the trigonal space group R3 with M = 440.8gmol^-1, Z = 27, R = 0.076, and wR = 0.145. The atomic arrangement found is that of a strongly deformed anti-CdI₂ type, but the deformation is clearly different from that given by previous workers. In the five crystallographically different STl₆ octahedra the S-Tl distances vary between 2.82 and 3.09 A, the Tl-Tl edges between 3.52 and 4.58 A. The common features of these octahedra are (i) each one with a definitely smaller vs larger Tl3 face in transposition, both faces parallel or sub-parallel (00.1), and (ii) each three shorter and longer S-Tl distances to the atoms of the larger and smaller Tl3 faces, respectively. The Tl-Tl contacts between different Tl₂S sheets are on the average definitely shorter than the ones within the sheet and they can be smaller than the Tl-Tl contacts in the small Tl3 faces of the STl₆ octahedra. The atomic arrangement indicates that the single electron pairs of the monovalent Tl atoms are not arranged all parallel to the z-axis, as one would expect for Tl₂S with an ideal anti-CdI₂ structure. The surrounding of the S atoms resembles that of one-third of the Cl atoms in yellow InCl. The absorbance of Tl₂S is very low at wave numbers approximately <9000 cm^-1.

Full text of DOI:10.1006/jssc.2002.9711

Journal of Solid State Chemistry 168, 322–330 (2002)
doi:10.1006/jssc.2002.9711
Tl2S: Re-Determination of Crystal Structure and Stereochemical
Discussion
G. Giester, C. L. Lengauer,1 E. Tillmanns, and J. Zemann
Institut fur Mineralogie und Kristallographie, Universita.t WienFGeozentrum, Althanstrasse 14, A-1090 Wien, Austria
.
Received March 28, 2002; in revised form June 21, 2002; accepted July 16, 2002
the high-temperature behavior of Tl2S up to approximately
The crystal structure of synthetic carlinite, Tl2S, was re- 7001C (4, 5) and its polymorphism dependency on synthesis
determined by single crystal and powder X-ray diffraction
methods. The cell parameters obtained from Rietveld refinement
conditions (6). As the accuracy of the papers cited does
not meet today’s standards, we decided to re-determine the
crystal structure of Tl2S to gain a better basis for a
stereochemical discussion.
3
(
(
(
are a = 12.150(2) A, c = 18.190(4) A, V = 2325.5(7) A .
A single crystal data refinement proved Tl2S crystallizing in
the trigonal space group R3 with M = 440.8 g molꢀ1, Z = 27,
R = 0.076, and wR = 0.145. The atomic arrangement found is
that of a strongly deformed anti-CdI2 type, but the deformation
is clearly different from that given by previous workers. In the
five crystallographically different STl6 octahedra the S–Tl
EXPERIMENTAL
In a first step, a fine powder of Tl2S was obtained by
reaction of TlNO3 with (NH4)2S. A strongly diluted,
alkaline solution of (NH4)2S was slowly added to an
aqueous solution of TlNO3 under continuous stirring at
301C till no further precipitation was observed. The
reaction product was washed several times with acetone
and dried under vacuum (o0.1 mbar) at room tempera-
ture. In the subsequent treatment the powder was heated
up to 6001C in a porcelain crucible inserted in a recipient
of quartz glass under improved vacuum conditions
(
distances vary between 2.82 and 3.09 A, the Tl–Tl edges between
(
3.52 and 4.58 A. The common features of these octahedra are (i)
each one with a definitely smaller vs larger Tl3 face in trans-
position, both faces parallel or sub-parallel (00.1), and (ii) each
three shorter and longer S–Tl distances to the atoms of the
larger and smaller Tl3 faces, respectively. The Tl–Tl contacts
between different Tl2S sheets are on the average definitely
shorter than the ones within the sheet and they can be smaller
than the Tl–Tl contacts in the small Tl3 faces of the STl6
octahedra. The atomic arrangement indicates that the single
electron pairs of the monovalent Tl atoms are not arranged all (o0.01 mbar). The melt was then slowly cooled for 6 h
parallel to the z-axis, as one would expect for Tl2S with an
to 4001C, kept for 12 h at this temperature, which is
ideal anti-CdI2 structure. The surrounding of the S atoms
resembles that of one-third of the Cl atoms in yellow InCl.
48 1C below a given melting point (7) or 501C below a
rhombohedral to hexagonal phase transition (5), and
finally cooled to room temperature within 6 h. The
obtained regulus showed a strong metallic lustre and was
composed of crystalline domains several mm in size. The
crystal fragments exhibited a perfect cleavage parallel to
(00.1) and could easily be deformed, which prohibited the
separation of crystals suitable for work on conventional
single-crystal diffractometers.
The absorbance of Tl2S is very low at wave numbers
approximately o9000 cmꢀ1
.
Key Words: Tl2S; carlinite; thallium stereochemistry; crystal
# 2002 Elsevier Science (USA)
structure refinement.
INTRODUCTION
By careful parting several thin platelets of Tl2S were
isolated and inspected by Weissenberg and Precession
photographs. Finally, a fragment with the approximate
dimensions 100 ꢁ 50 ꢁ 5 mm3 was selected for single-crystal
data collection. It was performed at room temperature
with a Nonius Mach3 CCD diffractometer equipped with a
0.3 mm capillary optics collimator. The measured inten-
sities were corrected for Lorentz and polarization effects,
and a numerical absorption correction was applied. A trial
Synthetic Tl2S is known to be a black, soft and extremely
platy substance. In nature it was described as the rare
mineral carlinite (1). Earlier crystal structure work (2, 3)
has shown that the atomic arrangement is similar to that of
the anti-CdI2 type, but with lattice parameters a and c
tripled. In the following, several investigations dealt with
1 To whom correspondence should be addressed. Fax: +431 4277 9532.
E-mail: christian.lengauer@univie.ac.at.
322
0022-4596/02 $35.00
r 2002 Elsevier Science (USA)
All rights reserved.

Tl2S: STRUCTURE AND STEREOCHEMICAL DISCUSSION
323
TABLE 1
Crystal Data and Structure Refinement for Tl2S
Crystallographic and sample data
Chemical formula
Data collection and reduction
Tl2S
440.8
trigonal
Temperature (K)
(
Radiation (A)
293
0.71073
Mol weight (g molꢀ1
Crystal system
Space group
)
y range (1)
hkl range
2.96-30.47
ꢀ17 o ho17
ꢀ17 o ko17
ꢀ25 o lo23
20756
R3 (no. 146)
12.150(2)
18.190(4)
2325.5(7)
27
(
a (A)
(
c (A)
3
(
V (A )
No. of measured F2o
Z
m(MoKa) (mmꢀ1
)
93.7
Density calc. (g cmꢀ3
Crystal form
Crystal size (mm3)
Crystal appearance
)
8.498
platelet
Absorption correction
No. of independent Fo2
No. of F2o>4s(F2o)
Rint F2o
numerical
3120
2449
0.1 ꢁ 0.05 ꢁ 0.005
metallic lustre
0.21
Single-crystal refinement
Rietveld refinement
F (000)
4806
84
2y range (1)
Imax (counts)
9–131
23 400
6101
28
No. of variables
Extinction coefficient
Ra
0.0004(1)
0.076
0.055
0.145
0.132
ꢀ2.6/2.4
1
No. of observations
No. of background points
No. of variables
No. of reflections
Rwp/Rpb
R for Fo>4s(Fo)
10
wRa
1839
7.6/4.7
12.5/9.4
wR for F2o>4s(F2o)
ꢀ3
(
(e A
r
)
Rp0/RBb
min/max
a
2
2 2
2
2
2
2
2
2
2
R = S||Fo|–| Fc||/S|Fo|, wR = [Sw(FoFFc) /S w|Fo| ] , w = 1/[s (Fo)+(0.05 ꢁ P) +170 ꢁ P], P = [max of (0 or Fo)]+2 Fc/3.
b R-values as defined by Hill and Fischer (32).
Note. Single-crystal equipment: Nonius Mach3 goniometer, CCD area detector, graphite monochromator, capillary optics collimator. Measurement:
28 mm crystal–detector distance, frames with 21 rotation width and 2 ꢁ 30 s exposure time/frame, one set of j and five sets of o scans (total 405 frames)
to complete whole sphere.
to refine the structural parameters given by Man (3) with reflections with yo24.51; R was now 0.039for 1014
least-squares methods failed. Therefore, the structure was F2o>4s(Fo2). Within the limits of accuracy the atomic
re-determined by direct methods. Information on crystal coordinates were the same as in Table 2, and the standard
data, procedures of measurements and refinements are deviations for the coordinates of the S atoms were even
compiled in Table 1. Programs used are Collect (8), Denzo- smaller, because at low diffraction angles the ratio of the
SMN (9), and SHELX-97 (10). Because of the poor quality scattering factors fS/fTl is larger than at high diffraction
of the crystals, the extremely platy nature and the high angles. As a consequence, there is no doubt that the
absorption, anomalous dispersion effects could not be reported structure is correct within the limits of accuracy
taken into account. This holds also for the investigation of given.
Friedel’s law violations. Refined structure parameters are
As the quality of the selected ‘‘best’’ suitable crystal did
listed in Table 2. This table also gives the atomic not allow a reliable determination of the cell parameters,
coordinates of an ‘‘ideal’’ Tl2S structure of the anti-CdI2 X-ray powder data using CuKa radiation were collected
type, in which the z coordinates of the S atoms are all equal on a Philips X’Pert MPD y–y diffractometer with
to zero and all Tl atoms have as absolute values of z the an automatic divergence slit, sample spinner, graphite
average of the arithmetic mean of the six absolute z (Tl) secondary monochromator, and a proportional counter.
values. In addition, the atomic shifts in space between the Due to the ductile properties and a rapid oxidation to
experimental and the ‘‘ideal’’ structure are listed. Accord- Tl2SO4 under ambient grinding conditions the
ing to the recommendation of Sheldrick (10) none of the z powder sample was prepared under liquid nitrogen and
coordinates were fixed during the refinement. The displace- immediately packed into a sample holder using the
ment parameters (Table 2) do not indicate that positions back-loading technique. For the cell refinement the
are only partly occupied, or should be split in appreciable program Pc-Rietveld Plus (11) was applied, using the
amounts.
atomic coordinates and isotropic displacement parameters
Because of the poor quality of the material the final R of the single-crystal structure refinement. As a distinct
value for F2o>4s(F2o) was only 0.055. We refined the texture parallel (00.1) was still evident in the X-ray powder
structure also with a restricted data set using only pattern, the region of the (00.6) reflection with a maximum

324
GIESTER ET AL.
TABLE 2
Atomic Coordinates and Equivalent Isotropic Displacement Parameters for Tl2S (first line), in Comparison
with the ‘‘ideal’’ Structure (second line)
2 b
c
(
Ueq (A )
(
Atom
Tl1
Site
x
y
za
D (A)
9b
0.1257(1)
0.1111
0.4685(1)
0.4444
0.8065(1)
0.7777
0.2407(1)
0.2222
0.5399(1)
0.5555
0.8712(1)
0.8888
0.0
0.2030(1)
0.2222
ꢀ0.0781(1)
ꢀ0.0914
ꢀ0.0969(1)
ꢀ0.0914
ꢀ0.0992(1)
ꢀ0.0914
0.1046(1)
0.0914
0.0457(4)
0.43(0.36)
0.28(0.26)
0.34(0.30)
0.35(0.26)
0.33(0.30)
0.36(0.34)
0.66(0.00)
0.46(0.00)
0.47(0.00)
0.49(0.07)
0.38(0.11)
Tl2
Tl3
Tl4
Tl5
Tl6
S1
9b
9b
9b
9b
9b
3a
3a
3a
9b
9b
0.9065(1)
0.8888
0.0452(4)
0.0449(4)
0.0451(4)
0.0453(4)
0.0457(4)
0.047(4)
0.047(3)
0.048(4)
0.041(2)
0.047(3)
0.5719(1)
0.5555
0.1060(1)
0.1111
0.7488(1)
0.7777
0.0846(1)
0.0914
0.4124(1)
0.4444
0.0
0.0850(1)
0.0914
0.0365(14)
0.0
0.0
0.0
0.6667
S2
0.3333
0.3333
0.6667
0.6667
0.0025(8)
0.0
ꢀ0.0255(10)
0.0
0.6667
0.3333
S3
ꢀ0.0261(10)
0.0
0.3333
0.6630(10)
0.6667
S4
0.0269(7)
0.0
S5
0.9992(9)
1.0
0.3234(10)
0.3333
ꢀ0.0200(6)
0.0
a To facilitate the comparison with the ‘‘ideal’’ structure, the origin of the experimental structure was chosen with an arithmetic mean of the z
coordinates of the Tl atoms in the Tl2S sheet around z = 0 equals to zero.
b Ueq is defined as one-third of the trace of the orthogonalized Uij tensor.
c Atomic shifts between experimental and ‘‘ideal’’ structure (for definitions see text), in this column the values in parentheses give the ‘horizontal’
component of the shift.
DESCRIPTION OF THE ATOMIC ARRANGEMENT
intensity about 10 times higher than the remaining
intensities was excluded from the refinement. A similar
powder pattern characteristic, however, with a wrong
indexing of (22.0), was reported in (1). The refined cell
parameters a = 12.150(2) A and c = 18.190(4) A agree
(
well with the range of reported values for a (12.12–12.22 A)
The results of our re-determination of the crystal
structure of Tl2S deviate from those published previously
(2, 3) in some essential features, although the structure can
still be considered to belong to a strongly deformed anti-
CdI2 type. As a consequence, a new description and a new
discussion of the stereochemistry seem to be needed.
Important interatomic distances and some bond angles
are given in Table 3, a projection of the structure parallel to
the x1-axis in Fig. 1, and a projection of a single ‘‘Tl2S
sheet’’ parallel to the z-axis in Fig. 2. In the description and
the discussion of the structure, interatomic distances will
(
(
(
and c (18.17–18.21 A) in the literature (1–3, 12). Due
to the higher accuracy, the cell parameters of the
Rietveld refinement were used in the final single-crystal
structure refinements and in the crystallochemical calcula-
tions.
Unpolarized absorption measurements were carried out
using a Bruker IFS 66v/S FTIR spectrometer with an
attached Bruker IRscope II microscope. The spectra were
recorded in the spectral range 15000 –650 cmꢀ1 using
different combinations of light sources (tungsten lamp,
globar), beam splitters (quartz, KBr) and detectors
(Ge-diode and liquid nitrogen cooled MCT). The resolu-
tion was set to 10 cmꢀ1 and the measuring diameter was
32 mm. Spectra were averaged over 128 scans. A phase
correction mode of the interferogram was performed
according to (13), cf. Griffiths and de Haseth (14). The
Norton–Beer weak mode was chosen as the apodization
function.
(
always be given to two decimals (so0.01 A), although for
the Tl–Tl distances three decimals would be adequate
(
(so0.005 A).
The geometry of the atomic arrangement in Tl2S is that
of a strongly distorted anti-CdI2 structure type, with both a
and c tripled. However, while in the anti-CdI2 type itself all
the S–Tl distances in the STl6 octahedra would be of equal
length, they vary in the experimentally determined struc-
(
ture from 2.82 to 3.09 A, i.e., by approximately 10%. The
Tl–Tl edges of the STl6 octahedra vary even more strongly,
this holds especially for the ones exactly or approximately

Tl2S: STRUCTURE AND STEREOCHEMICAL DISCUSSION
325
TABLE 3
(
2
(
Selected Interatomic Distances (A), Angles (1) and Areas (A ) for Tl2S
S1–Tl4 (3 ꢁ )
S1–Tl1 (3 ꢁ )
2.82a
3.00b
S2–Tl5 (3 ꢁ )
S2–Tl2 (3 ꢁ )
2.97a
2.84b
S3–Tl6 (3 ꢁ )
S3–Tl3 (3 ꢁ )
2.97a
2.85b
S4–Tl5
S4–Tl6
S4–Tl4
S4–Tl1
S4–Tl2
S4–Tl3
2.82a
2.84a
2.85a
2.96b
3.03b
3.09b
S5–Tl5
S5–Tl6
S5–Tl4
S5–Tl1
S5–Tl3
S5–Tl2
2.94a
2.99a
3.02a
2.80b
2.86b
2.89b
Tl4–Tl4
Tl1–Tl1
Tl1–Tl4
Tl1–Tl4
4.40c
3.73d
4.00e
4.16e
Tl5–Tl5
Tl2–Tl2
Tl2–Tl5
Tl2–Tl5
3.79c
4.38d
4.02e
4.12e
Tl6–Tl6
Tl3–Tl3
Tl3–Tl6
Tl3–Tl6
3.76c
4.37d
4.07e
4.14e
Tl4–Tl5
4.52c
Tl5–Tl6
Tl5–Tl4
Tl6–Tl4
Tl1–Tl3
Tl1–Tl2
Tl3–Tl2
Tl5–Tl1
Tl5–Tl2
Tl6–Tl3
Tl6–Tl2
Tl4–Tl1
Tl4–Tl3
3.85c
3.91c
3.54c
4.34d
4.58d
4.25d
4.05e
4.02e
4.07e
4.08e
4.16e
4.22e
c
Tl4–S1–Tl4
Tl1–S1–Tl
Tl1–S1–Tl4
Tl1–S1–Tl4
102
177
91
Tl5–S2–Tl5
Tl2–S2–Tl2
Tl2–S2–Tl5
Tl2–S2–Tl5
79Tl6–S3–Tl6
79Tl4–Tl6
Tl3–S3–Tl3
Tl3–S3–Tl6
4.27
101
87
100
89
Tl5–Tl6
Tl1–Tl2
Tl1–Tl3
Tl2–Tl3
Tl5–Tl1
Tl5–Tl2
4.61c
3.91d
3.52d
3.55d
4.05e
87
90
Tl3–S3–Tl6
91
Tl–Tl contacts between the Tl2S sheets (oTl–Tl>=3.63)
4.12e
e
Tl1–Tl4
Tl1–Tl6
Tl1–Tl6
3.64
3.77
3.78
Tl2–Tl4
Tl2–Tl4
Tl2–Tl5
3.48
3.50
3.63
Tl3–Tl5
Tl3–Tl6
Tl3–Tl5
3.59Tl6–Tl2
3.63
3.63
4.08
Tl6–Tl3
Tl4–Tl1
Tl4–Tl3
4.14e
4.00e
4.22e
Areas of Tl3 triangles parallel (00.1)
(i) faces of the STl6 octahedra
Tl5–S4–Tl6
Tl5–S4–Tl4
Tl6–S4–Tl4
Tl1–S4–Tl2
Tl1–S4–Tl3
Tl2–S4–Tl3
Tl5–S4–Tl1
Tl5–S4–Tl2
Tl6–S4–Tl2
Tl6–S4–Tl3
Tl4–S4–Tl1
Tl4–S4–Tl3
109Tl5–S5–Tl6
81
106
97
Tl5–S5–Tl4
Tl6–S5–Tl4
Tl1–S5–Tl3
Tl1–S5–Tl2
Tl3–S5–Tl2
82
72
Around S1
Around S2
Around S3
Around S4
Around S5
Tl1–Tl1–Tl1
6.04
6.22
6.12
5.76
6.11
Tl4–Tl4–Tl4
Tl2–Tl2–Tl2
Tl3–Tl3–Tl3
Tl4–Tl5–Tl6
Tl1–Tl2–Tl3
8.73
8.31
8.27
8.61
8.10
Tl5–Tl5–Tl5
Tl6–Tl6–Tl6
Tl1–Tl2–Tl3
Tl4–Tl5–Tl6
82
71
100
107
96
71
89Tl5–S5–T0l1
9
90
88
88
87
91
Tl5–S5–Tl2
Tl6–S5–Tl3
Tl6–S5–Tl2
Tl4–S5–Tl1
Tl4–S5–Tl3
87
88
88
91
92
(ii) not faces of the STl6 octahedra
Tl1–Tl1–Tl3
Tl2–Tl2–Tl1
6.30
7.88
Tl3–Tl3–Tl2
Tl4–Tl4–Tl5
6.97
7.83
Tl5–Tl5–Tl6
Tl6–Tl6–Tl4
7.02
6.31
a To Tl atom ‘‘above’’ the S atom.
b To Tl atom ‘‘below’’ the S atom.
c Within the plane ‘‘above’’ the S atom.
d Within the plane ‘‘below’’ the S atom,
e Common edges between the STl6 octahedra in the Tl2S sheet, arithmetic mean: 4.10(7) A.
(
(
Note. Errors for the S–Tl distances o0.01, the Tl–Tl distances o0.005 A, and for all bond angles o0.51; arithmetic means over all five STl6 octahedra
(
of the three shorter/longer S–Tl distances: 2.84(2)/2.99(4) A; of the Tl–Tl edges in the smaller / larger Tl3, triangles parallel (00.1): 3.73(16) / 4.40(15) A.
(
parallel to (00.1). In the anti-CdI2 type they would all be of which each Tl atom forms the apex of a TlS3 pyramid are
equal length, in the experimental structure, however, they stacked along the z-axis according to the R centering.
(
vary from 3.52 to 4.61 A, i.e., by approximately 30% (!). In Therefore, each Tl atom has, in addition to its nine Tl
the cases where it is not forbidden by symmetry they vary neighbors within the sheet, three more Tl contacts to a
by approximately 10% even within such individual Tl3 neighboring sheet to complete a strongly distorted 12-
triangles. All five crystallographically different types of coordination of Tl atoms. The histograms of Fig. 3 show
STl6 octahedra in Tl2S have two Tl3 faces exactly or that the Tl–Tl contacts within the Tl2S sheet split up into
approximately parallel to (00.1). Contrary to the anti-CdI2 three classes:
type, one of the two is always distinctly larger, approxi-
mately by one-fourth in area (Table 3). This deformation
of the STl6 octahedra has one kind of orientation around
S1 and S4 and another one around S2, S3 and S5. The
(
(i) edges of the small Tl3 faces parallel (00.1) 3.73(16) A;
(
(ii) edges of the large Tl3 faces parallel (00.1) 4.40(15) A;
(
(iii) oblique edges in the STl6 polyhedra 4.10(7) A.
They further show that the Tl–Tl contacts between
neighboring Tl2S sheets are relatively short, namely
(
3.62(10) A (see second paragraph of ‘‘Discussion’’), and
the 12-coordination of the Tl atoms is so strongly distorted
shorter S–Tl distances always point to atoms of the larger
Tl3-triangle (Table 3).
In spite of the greatly varying Tl–Tl distances the Tl2S
sheet is rather flat. Geometrically identical Tl2S sheets in

326
GIESTER ET AL.
(
that (in addition to three close S neighbors at 2.80–3.09 A)
each Tl atom has at least one S-neighbor at a distance
smaller than that to the most distant neighbor in the 12-
coordination to Tl atoms.
It should be noted that for a theoretical Tl2S structure of
the ‘‘ideal’’ anti-CdI2 type (Table 2) the histogram of the
distances around Tl in Fig. 3 would give only three Tl–Tl
(
(
signals: at 4.05 A (multiplicity 6), at 4.06 and at 3.60 A
(both with multiplicity 3). The Tl–Tl contacts between
different ‘‘Tl2S sheets’’ in the experimental structure are
relatively short (see above). From this point of view it is
somewhat misleading to speak of a stacking of ‘‘Tl2S
sheets’’. A way to avoid this would be to consider the
atomic arrangement to be a distorted hexagonal close
packing of Tl atoms with S atoms occupying octahedral
voids in layers parallel to (00.1). In this context it seems
interesting to note that also in the 2H-modification of PbI2,
which corresponds to the simple CdI2 type, the I–I edges of
(
the PbI6 octahedron (4.447, 4.573 A, each 6 ꢁ ) are all
(
longer than the interlayer I–I contacts (4.177 A) (15).
DISCUSSION
Of the earlier structural work on Tl2S a more detailed
comparison is possible only with the electron-diffraction
study by Man (3). The atomic arrangement determined by
us deviates from that given by Man not merely by minor
FIG. 1. Ball and stick projection of the atomic arrangement in Tl2S
(
along x1 with Tl (dark gray), S (light gray balls), Tl–S o2.90 A (thick),
(
(
and 2.90 AoTl–So3.10 A (thin sticks).
FIG. 2. Ball and stick projection of the Tl2S sheet with –0.10 ozo+0.10 along z. Same symbols as in Fig. 1.

Tl2S: STRUCTURE AND STEREOCHEMICAL DISCUSSION
327
(
shortest Tl–Tl contact (= 3.48 A) compares well with
analog values from the literature. Shorter Tl–Tl contacts
have been reported for monovalent and for metallic
(
thallium only rarely: hexagonal Tl (3.40, 3.45 A: 16), cubic
(
Tl (3.36 A: 16), tetragonal Tl(TlS4) (3.40 A: 17), Tl4SnS4
(
(
(
(3.44, 3.46 A: 18), Tl7Sb2 (3.21, 3.43 A: 19). The lengths of
the contacts of the Tl atoms to their neighbors vary greatly
(Fig. 3) as is common for monovalent thallium (see, e.g.,
20, 21). All five kinds of S atoms have a clear-cut, although
considerably distorted, octahedral coordination of Tl
(
atoms with S–Tl = 2.80–3.09 A. Up to now this kind of
Tl coordination around S seems not to have been found in
any other compound. The gap to further Tl neighbors is
(
(
Z1.16 A.The shortest S–Tl contact (2.80 A) belongs to the
smallest ones reported in the literature, i.e., in Tl2Sn2S3
(
(2.81(2) A: 20), but slightly larger ones are quite common,
(
e.g., in Tl4SnS3 (2.87(3), 2.88(7) A: 22), in jankovicite,
(
Tl5Sb9(As1Sb)4S22 2.890(4) A: 23), and in lorandite, TlAsS2
(
(2.91(2) A: 24). It seems worth noting that the average S–Tl
(
distance in the STl6 octahedra in Tl2S (2.92 A) is smaller
than the S–Pb distance in the SPb6 octahedron of galena,
(
PbS (2.97 A).
FIG. 3. Histograms of the contacts of the six kinds of Tl atoms to their
neighbors. The contacts to the three nearest S neighbors, i.e., to those with
(
Tl–S r2. 89 A, are always omitted. Full lines: Tl neighbors. No signature:
small Tl3 triangles of the STl6 octahedra; circles: large Tl3 triangles in the
STl6 octahedra; triangles: common Tl–Tl edges in the Tl2S sheet (labelled e
in Table 3); crosses: Tl–Tl contacts between neighboring Tl2S layers. Note
that Tl1, Tl5 and Tl6 belong each to one large and two small Tl3 triangles
parallel to the sheet, while Tl2 and Tl3 belong to one small and two large
Tl3 triangles. Dotted lines: Tl–S contacts to S atoms of neighboring STl6
octahedra.
atomic shifts. This is most clearly seen in the sequence of
the main distortions of the three crystallographically
different STl6 octahedra with point symmetry 3 along the
z-axis (Fig. 4). According to Man (3) all three have the
same direction, but we found that only two of them have
the same direction, while the third has the opposite one. It
is to be noted that our structure is considerably better
proven than that by Man (3) as she obtained
R(h,0,l) = 0.294 and did not publish standard deviations
of the atomic coordinates.
FIG. 4. Sequence of the main ‘‘up–down’’ distortions of the three
kinds of STl6 octahedra with symmetry 3 along the three-fold axis (a)
according to the present investigation and (b) according to Man (1970).
Schematically.
The interatomic distances in Tl2S (Table 3) agree with
the experience from other inorganic compounds. The

328
GIESTER ET AL.
computations (25) failed when using in the STl6 octahedra
one weight each for the smaller and larger S–Tl distances,
the oblique Tl–Tl distances, the Tl–Tl distances of the small
and of the large Tl3 triangles parallel to (00.1) and one
weight for all ‘‘inter-layer’’ Tl–Tl distances. In the ideal
anti-CdI2-type the lone electron pairs of Tl(I) would all be
oriented exactly parallel to the z-axis. From the experi-
mentally determined structure this is, however, not
indicated, e.g. because in none of the five TlS3 pyramids
the three S-Tl bonds are of equal length. The observation
that Tl2S becomes transparent for electromagnetic radia-
tion at wave numbers o9000 cmꢀ1 (Fig. 5) indicates that it
is a semiconductor with an energy gap of approximately
1 eV (26).
A comparison would be interesting with A[6B]B2[3A] com-
pounds of atoms with the same electron configuration in
the outermost atomic shell as in S and Tl, respectively,
especially with Tl2O, Tl2Se, and In2S. Unfortunately, this is
hardly possible. For Tl2O only the main features of the
FIG. 5. IR-absorption spectrum of Tl2S for the ordinary wave.
Although the chemical formula of Tl2S is very simple, its atomic arrangement are known with certainty (27, 28).
atomic arrangement is rather complex. There occur six Although the Tl atoms are arranged essentially in the
crystallographically different kinds of Tl atoms (all of point hexagonal close packing as in Tl2S, the two compounds are
symmetry 1) and five different kinds of S atoms (three of definitely not isostructural in detail. It seems worthwhile to
point symmetry 3, and two of point symmetry 1). In spite note that for the pseudo-cell corresponding to the
of their crystallographic diversity, the surroundings of the hexagonal close packing, c/a = 1.80 for Tl2O, but 1.50
different kinds of Tl atoms, as well as those of the S atoms, for Tl2S. The structure of stoichiometric Tl2Se does not
are geometrically not essentially different. seem to be reliably determined, and In2S apparently is not
This raises the question of the possibility to build anti- even a stable solid phase.
CdI2 sheets from equal STl6-octahedra of local symmetry
It seems worth noting that in the yellow (= room-
3, each with one ‘‘large’’ and one ‘‘small’’ equilateral Tl3- temperature) modification of InCl (29, 30) several stereo-
triangle parallel to (00.1). Geometric analysis shows that chemical features are similar to those in Tl2S. In spite of the
this is not possible (see Appendix A). In agreement with simple formula InCl has a complex crystal structure, i.e., a
this theoretical result the edge lengths within the non- strongly distorted NaCl type with the lattice parameter
symmetry-restricted Tl3 faces parallel to (00.1) vary by doubled, space group P213, Z = 32 (29, 30). An extensive
approximately 10%.
discussion of the atomic arrangement, stressing the role of
Since in all five kinds of STl6 octahedra the S atom is stereochemically active (5 s)2 lone pairs of the In atoms,
shifted towards the larger one of the basal Tl3 faces, it is was given by van der Vorst and Maaskant (31). Of special
further interesting to learn which kinds of trigonal ‘‘up– interest here are the four kinds of distorted ClIn6
down’’ patterns are possible. This holds especially for an octahedra. Five-eighths of them have the exact or
‘‘up–down’’ ratio of exactly or approximately 1:1, because approximate symmetry 3, while the remaining three-eighths
for such ‘‘up–down’’ ratios the tension between the have the approximate symmetry 2 (29, 30); in Tl2S,
‘‘upper’’ and ‘‘lower’’ Tl plane is expected to be relatively however, all STl6 octahedra have the exact or approximate
small. Results of the geometric analysis for not too large symmetry 3. A common feature of all known ClIn6 and
identity periods are presented in Appendix B. Curiously STl6 octahedra with symmetry or pseudo-symmetry 3 is
enough, the ‘‘up–down’’ pattern of the experimental that three shorter bonds go to a clearly larger face of the
structure does not correspond to a 1:1 pattern, and, octahedron than the three longer bonds.
therefore, also not to the 1:1 pattern with the smallest
possible cell, but to the smallest possible 4:5 pattern. This is
possibly connected with the peculiarity that in the 1:1
ACKNOWLEDGMENTS
pattern the Tl atoms of one-sixth of the STl3 pyramids have
no short bonds to neighboring STl3 pyramids, while this is
always the case for the 4:5 pattern.
The authors thank Dr. M. Andrut and Prof. M. Wildner, who kindly
provided the IR measurements and also Ing. W. Zirbs, for his help in
Trials to derive the experimental structure from the one
of the undistorted anti-CdI2 type by distance least-squares reviewers have improved the manuscript.
preparing the illustrations. The constructive comments of the JSSC

Tl2S: STRUCTURE AND STEREOCHEMICAL DISCUSSION
329
APPENDIX A
Proof that one cannot build a distorted anti-CdI2 type
from identical octahedra with local symmetry 3 or 3m:
The octahedral sheet should have properties as follows:
(i) It is built from isometric octahedra with local symmetry
3 or 3m. The two faces perpendicular to the three-fold axis
can have different sizes (Fig. A1), (ii) each corner belongs
to three octahedra, and (iii) at each corner six edges meet
parallel to the sheet.
FIG. A2. Rings of three AB6 octahedra of which two have the same
kind of up-down orientation. (a) The octahedra B and B0 have symmetry
3. (b) The octahedra have symmetry 3m, the angles a, b, and g are in the
Every such possible sheet has two nets of equilateral
triangles: a ‘‘lower’’ and an ‘‘upper’’ one. The triangles of
the sheets have no edges in common, but each three sides plane of drawing. For further explanation see text.
meet in one point; every ring of three triangles is necessarily
rigid. There exist two principally different cases: (i) all
triangles of a net have equal size, and (ii) the net has
triangles of two different sizes.
APPENDIX B. ‘‘UP-DOWN’’ ORDERINGS
IN Tl2S SHEETS
Case (i) is simple. Let us suppose that the three larger
triangles of the configuration are at the one side of the
sheet. The corresponding configuration with the three
smaller triangles is then necessarily on the other side. As
both configurations are rigid and of different size, they do
not fit on each other.
In the STl6 octahedra of the Tl2S sheets the S atoms are
shifted from the centers up or down in approximately equal
amounts. Such arrangements can be symbolized by black
and white octahedra in a CdI2-type sheet. The smallest
possible such pattern with trigonal symmetry and equal
amounts of black and white octahedra is presented in
Fig. B1(a). The cell contains each six black and six white
Case (ii) requires more detailed considerations. Figure
A2(a) shows a ring of three octahedra. The isometric
octahedra B and B0 have symmetry 3 and share the edge
P–P0. The octahedron A shares the edges P–Q and
P–R with the octahedra B and B0. As P–Q and P–R have
the same length, the octahedron A cannot have symmetry
3, but has to have symmetry 3m. As it was further
presumed that all octahedra have the same symmetry, the
octahedra B and B0 also have to have symmetry 3m.
Figure A2(b) is not greatly different from Fig. A2(a).
But now all three octahedra A, B and B0 have symmetry
3m. Because b = 2401-a, and the three octahedra have
necessarily the same outline, we have at point P:
g = 3601ꢀ2a = 2401ꢀa. As a consequence a = 1201 and
the (empty) octahedra A, B, and B0 are identical and have
ꢀ
symmetry 32/m.
FIG. B1. Two black–white ordering patterns of AB2 sheets as in Tl2S.
(a) Pattern with black:white=1:1 and the smallest possible unit cell. (b)
Pattern with black:white=1:1 and the smallest possible unit cell. (b)
Pattern with black:white=4:5, corresponding to the up-down ordering of
the distortions of the STl6 octahedra in Tl2S.
FIG. A1. AB6 octahedra projected parallel to the 3-fold axis. (a) With
symmetry 3; (b) with symmetry 3m.

330
GIESTER ET AL.
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