Electronic properties of the crystalline phases of the Sb2S3-Tl2S system

Article abstract of DOI:10.1103/PhysRevB.56.13054

The electronic properties of the crystalline phases of the Sb₂S₃-Tl₂S system are investigated both experi-mentally and theoretically. Experimental data obtained by x-ray photoelectron spectroscopy and ¹²¹Sb Moes

Full text of DOI:10.1103/PhysRevB.56.13054

PHYSICAL REVIEW B
VOLUME 56, NUMBER 20
15 NOVEMBER 1997-II
Electronic properties of the crystalline phases of the Sb2S3-Tl2S system
*
P. E. Lippens, J. Olivier-Fourcade, and J. C. Jumas
`
´
´
`
Laboratoire de Physicochimie de la Matiere Condensee, CNRS UMR 5617, Universite Montpellier II, Place Eugene Bataillon,
´
F-34095 Montpellier Cedex 05, France
´ ´
A. Gheorghiu, S. Dupont, and C. Senemaud
`
´
Laboratoire de Chimie-Physique, Matiere et Rayonnement, CNRS URA 176, Universite Paris VII, 11, rue Pierre et Marie Curie,
´
F-75231 Paris Cedex 05, France
͑Received 5 March 1997͒
The electronic properties of the crystalline phases of the Sb2S3-Tl2S system are investigated both experi-
121
¨
mentally and theoretically. Experimental data obtained by x-ray photoelectron spectroscopy and Sb Moss-
bauer spectroscopy are reported and analyzed from tight-binding calculations, which are used here because of
the complexity of the materials. The main features of the x-ray photoelectron valence bands and S K␤
emission spectra are identified. The binding energy of the S 2p3/2 core level is found to decrease from Sb2S3
121
¨
to Tl2S in agreement with the variations of the calculated S charges. We show that the Sb Mossbauer isomer
shift and the surface of the prepeak observed in x-ray-absorption spectra at the Sb LIII edge can be linearly
correlated because they are both strongly dependent on the Sb 5s electron population. Finally, analytical
expressions of the numbers of Sb and S valence electrons are derived from simple molecular calculations.
These expressions provide rather simple explanations for the observed main trends in the variations of the
experimental results in terms of local structural changes. ͓S0163-1829͑97͒06543-0͔
I. INTRODUCTION
contribution of the Sb 5s states to the conduction bands of
the glassy and crystalline compounds of the As2S3-
Sb2S3-Tl2S system.13 The XAS spectra exhibit a prepeak at
the absorption edge, which has been attributed to the Sb 5s
empty states. The prepeak amplitude is found to increase
from Sb2S3 to Tl3SbS3 indicating an increase in the contri-
bution of the Sb 5s empty states. The S K␤ x-ray-emission
spectroscopy ͑XES͒ has been used to investigate the S 3p
valence-band states.14 The XES spectra are formed by a
broad asymmetric band. The width of this band decreases
and a well-resolved shoulder occurs at the low transition-
energy side with increasing content of Tl atoms. The results
obtained from these two experiments have been qualitatively
explained from changes in the local environments of Sb and
S atoms, respectively.
Ternary chalcogenides of thallium form an interesting
family of materials because of their potential optoelectronic
applications. Many studies concern layered compounds of
the form TlAB2 , where A stands for an element of columns
III or V and B represents a chalcogen. For example physical
properties of TlInS2,1,2 TlInSe2,2,3 TlGaS2,2,3 TlGaSe2,3,4
and TlSbS2 ͑Ref. 5͒ have been extensively investigated be-
cause of the structural anisotropy of these materials. There is
also a particular interest for compounds of the form
Tl3AB3 .6 For example, Tl3AsSe3 has been proposed as a
candidate for nonlinear optical and acousto-optic
applications.7 The interesting results obtained for these two
classes of materials suggest further investigations in other
thallium chalcogenides.
This paper concerns the crystalline phases of the
Sb2S3-Tl2S system. Previous works have unambiguously
shown the existence of four ternary crystalline phases:8–11
TlSb5S8, TlSb3S5, TlSbS2, and Tl3SbS3. Their structures are
rather complex showing different crystallographic sites for
each of the three atoms. The Sb atoms are found to be sur-
rounded by three, four, or five S atoms as nearest neighbors.
The local environments of the Tl atoms are more complex in
relation with their ionic character. From the chemist’s point
of view, addition of Tl2S to Sb2S3 increases the covalent
character of the Sb-S bonds and decreases the ionic character
of the Tl-S bonds. This can be related to changes in the
dimensionality of the antimony compounds from Sb2S3,
which is a chainlike compound to Tl3SbS3, which can be
described by a three-dimensional network.12
In this paper we report new experimental results obtained
by x-ray-photoemission spectroscopy ͑XPS͒ and 121Sb
¨
Mossbauer spectroscopy. These results as well as those ob-
tained by XAS and XES are discussed from a tight-binding
method. This approach is used here because of the complex-
ity of the crystalline phases of the system Sb2S3-Tl2S. In
addition, tight-binding theory has been shown to provide cor-
rect variations in the electronic properties of very different
materials including chalcogenides.15–19 The main features of
the valence bands obtained by XPS and S K␤ XES are ana-
lyzed from the contributions of the atomic orbitals. Varia-
tions of the core-level binding energies measured by XPS are
found to be consistent with changes in the calculated atomic
121
¨
charges. Finally, we show that variations of the Sb Moss-
bauer isomer shift and the surface of the prepeak observed in
XAS spectra at the Sb LIII edge can be correlated because
they are both strongly dependent on the Sb 5s electron popu-
lation.
The electronic properties of the ternary compounds have
been partially investigated. The x-ray-absorption spectros-
copy ͑XAS͒ at the Sb LIII edge has been used to study the
We focus our interest on the effect of structural changes
0163-1829/97/56͑20͒/13054͑12͒/$10.00
56
13 054
© 1997 The American Physical Society

56
ELECTRONIC PROPERTIES OF THE CRYSTALLINE . . .
13 055
TABLE I. Space groups and numbers of atoms per cell Nat of the crystalline phases of the Sb2S3-Tl2S
system.
a
b
c
d
e
Sb2S3
TlSb5S8
TlSb3S5
TlSbS2
Tl3SbS3
Tl2Sf
Rhombohedral
R3
Space
groups
Orthorhombic
Monoclinic
Monoclinic
Triclinic
Rhombohedral
Pnma
Pn
P21 /c
P1
R3m
Nat
20
56
36
16
21
81
aReference 20.
bReference 8.
cReference 9.
dReference 10.
eReference 11.
fReference 21.
in the local environments of Sb and S atoms onto the elec-
tronic properties. Molecular calculations are proposed in or-
der to relate the numbers of valence electrons for these two
atoms to their local environments. Considering only the main
interatomic interactions we have derived simple analytical
expressions that are able to explain the main trends in the
local electronic properties in terms of atom coordination
numbers and bond lengths.
SbS3 trigonal pyramids and two SbS5 square base pyramids
connected by threefold coordinated S atoms. The Sb4S6 units
are linked by twofold coordinated S atoms and form the
(Sb4S6)n chains. There are two and three distinct crystallo-
graphic sites for Sb and S, respectively. TlSb5S8 is formed by
(Sb5S8)n double layers parallel to the ͑101͒ axis.8 There are
ten different crystallographic sites for the Sb atoms, which
are in very distorded octahedral environments and are in fact
surrounded by three, four, and five S atoms as nearest neigh-
bors. There are 16 sites for the S atoms, which are strongly
bounded to two or three Sb atoms. The layers are connected
by long Sb-S bonds ͑Ͼ3.37 Å͒ and via Tl atoms. The Tl
atoms occupy two different crystallographic sites and are
surrounded by more than eight S atoms, suggesting a strong
ionic character for the Tl-S bonds. TlSb3S5 is a layered
compound.9 There are one, three, and five different crystal-
lographic sites for Tl, Sb, and S, respectively. Two Sb sites
are surrounded by three S atoms in trigonal pyramidal envi-
ronments, the third Sb site forms a trigonal bipyramid with
four S atoms. These SbS3 and SbS4 units form infinite layers
connected by the longest Sb-S bonds of the bipyramids ͑2.85
Å͒. The Tl atoms are found in the layers and are surrounded
by eight S atoms. TlSbS2 is a layered compound.10 Each
layer is formed by covalent chains containing Sb and S at-
oms which are linked together by long Sb-S bonds ͑3.7 Å͒
and ionic Tl-S bonds ͑3.4 Å͒. The chains are built up from
SbS4 distorted trigonal bipyramids connected by two twofold
coordinated S atoms. There are two, two, and four different
crystallographic sites for Sb, Tl, and S, respectively. The
structure of Tl3SbS3 can be described by a hexagonal close
packing of Tl and S atoms with intercalated Sb atoms.11 The
structure is rhombohedral and each atom occupies one crys-
tallographic site. The Sb atoms are surrounded by three S
atoms as nearest neighbors that form SbS3 trigonal pyramids.
The SbS3 units are linked together by S-Tl-S bridges and
form a three-dimensional network because of the partial co-
valent character of the Tl-S bonds. Tl2S is a distorted hex-
agonal close-packed arrangement of Tl atoms in which the
octahedral intertices between pairs of planes of Tl atoms are
occupied by S atoms.21 The structure is rhombohedral. There
are six and five different crystallographic sites for Tl and S,
respectively. The Tl atoms are surrounded by three S atoms
at distances in the range 2.5–3.3 Å, suggesting a more cova-
lent character for the Tl-S bonds in Tl2S than in ternary
compounds.
Section II concerns the synthesis and some structural as-
pects of the crystalline phases of the Sb2S3-Tl2S system. Ex-
¨
perimental aspects of the XPS and Mossbauer measurements
are given in Sec. III. The tight-binding scheme used in this
paper is detailed in Sec. IV. The experimental data are re-
ported and analyzed in Sec. V. The observed main trends in
the variations of the local electronic properties are discussed
in terms of the Sb and S environments from simple molecu-
lar calculations in Sec. VI. Finally, Sec. VII is devoted to
conclusions.
II. SYNTHESIS AND STRUCTURES
The crystalline phases of the Sb2S3-Tl2S system were pre-
pared by direct synthesis in fused silica tubes evacuated to
about 10Ϫ5 Torr. Sb2S3 was obtained from high-purity Sb
and S elements heated to about 600 °C for about 1 week and
then slowly cooled. Tl2S was prepared from Tl and S ele-
ments under Ar atmosphere in order to avoid oxydation. The
melt was heated during 3 days and slowly cooled. TlSbS2
and Tl3SbS3 were obtained from Tl2S and Sb2S3 heated dur-
ing 3 days at a temperature of about 500 and 600 °C, respec-
tively. TlSb3S6 was obtained from Sb2S3 and TlSbS2 at a
temperature of 380 °C for 3 weeks followed by a slow cool-
ing. For TlSb5S8 a glass with the same composition was first
prepared by quenching a melt of Sb2S3 and Tl3SbS5 in water.
The crystalline phase was obtained by annealing the glass at
254 °C for 3 weeks. All the compounds were finely grounded
for the experimental studies and their structures were con-
trolled by x-ray diffraction.
All
the
crystalline
structures
have
been
determined8–11,20,21 and the main informations used for the
analysis of the experimental data are reported in Table I.
This table shows that the structural complexity of the mate-
rials is mainly due to the great number of atoms per unit cell
and to the low lattice symmetry.
Sb2S3 is a ribbonlike material formed by (Sb4S6)n chains
parallel to the c axis.20 The Sb4S6 units are formed by two

13 056
P. E. LIPPENS et al.
56
and analyzed with an electrostatic hemispherical analyzer in
the FAT ͑fixed analyzer transmission͒ mode. The spectrom-
eter resolution was estimated from the Ag 3d5/2 energy to be
0.8 eV. Since our compounds are insulators, a charging ef-
fect was observed that induced a shift of the photoelectron
spectra towards a higher binding-energy scale. This effect
was corrected by shifting the binding-energy scale in order to
set the C 1s peak due to the superficial hydrocarbonated
contamination to 285.0 eV. In these conditions the origin of
the binding-energy scale corresponds to the Fermi level of
the sample. In the case of samples containing Tl atoms the
excitation of the Tl 5d3/2,5/2 core levels at binding energies of
about 13–15 eV by Mg K␣ satellite lines, namely, K␣3 ,
K␣Ј, and K␣4 , gives lower-intensity peaks that are precisely
located in the energy range of the valence band. Conse-
quently, a correction was achieved to subtract these contri-
butions from the total photoelectron spectra. Because the
samples were powders and due to the low values of the pho-
toemission cross sections for Sb and Tl valence states, we
FIG. 1. Schematic description of the basic SbSn units found in
the crystalline phases of the Sb2S3-Tl2S system. The units are trigo-
nal pyramids SbS3, trigonal bipyramids SbS4, and square base pyra-
mids SbS5.
The previous description of the crystalline structures
shows that the local environments of the Sb atoms can be
described by SbSn units with nϭ3 ͑trigonal pyramids͒, n
ϭ4 ͑trigonal bipyramids͒, and nϭ5 ͑square base pyramids͒
͑Fig. 1͒. The numbers of SbSn units and the average Sb-S
bond lengths of the antimony compounds studied in this pa-
per are given in Table II. It is worth noticing that the values
of the average Sb-S bond lengths are close to the sum of the
covalent radii defined by Pauling22 ͑2.4 Å͒. The average
Sb-S bond length decreases from 2.62 Å (Sb2S3) to 2.43 Å
(Tl3SbS3), suggesting a slight increase in the covalency of
the Sb-S bonds with increasing Tl2S content. The values of
the average Tl-S bond lengths are close to the sum of the
ionic radii defined by Pauling22 ͑3.3 Å͒ and decrease from
3.25 Å (TlSb5S8) to 2.87 Å (Tl2S), suggesting a decrease in
the ionicity of the Tl-S bonds. In fact the situation is more
complicated for Tl3SbS3 and Tl2S because the average Tl-S
bond lengths of 3.03 Å and 2.87 Å, respectively, indicate a
partial covalent character for the Tl-S bonds. This is consis-
tent with the observed low coordination number for the Tl
atoms in these two compounds ͑3–5͒ compared with the Tl
coordination numbers in the other three ternary compounds
͑5–7͒. In the six crystalline phases the SbSn units are con-
nected by twofold and threefold coordinated S atoms in order
to form covalent networks.
obtained XPS valence-band spectra of low intensity.
121
¨
The
Sb Mossbauer spectroscopy measurements were
performed with a Elscint AME 40 spectrometer at liquid-
Helium temperature for both the absorber and the source. A
500 ␮Ci source of 37.2 keV ␥ rays was obtained from Ba
121SnO3. The absorbing materials were obtained from pow-
dered samples mixed with Apiezon jelly ͑grease͒ and con-
taining approximately 1 mg/cm2 of 121Sb. The spectra were
recorded during one day for a good signal-to-noise ratio. The
velocity calibration was obtained by using a 57Co source and
¨
a high-purity iron foil absorber. The Mossbauer parameters:
isomer shift ␦, quadrupole splitting ⌬, and linewidth ⌫ were
¨
obtained by a nonlinear least-squares fit of the Mossbauer
spectra with the computer program of Ruebenbauer and
Birchall.23
The S K␤ XES measurements were carried out at LURE
͑Orsay, France͒ in order to probe the partial S 3p density of
states. The XAS spectra at the Sb LIII edge were recorded
using the synchrotron radiation of the DCI storage ring ͑Or-
say, France͒. Details on the measurements and a qualitative
discussion of the results can be found elsewhere.13,14 The
results obtained from these two techniques are considered in
this paper for a complete discussion in relation with the XPS
III. EXPERIMENTS
The XPS is used to obtain information on the binding
energies of the core levels and on the densities of states
͑DOS͒ of the valence bands. The photoelectron spectra were
excited by using a Mg anode x-ray tube (h␯ϭ1253.6 eV)
¨
and Mossbauer data. It is worth noticing that all the experi-
ments were carried out on the same powdered samples.
TABLE II. Average Sb-S interatomic distances ͑in Å͒ and numbers of SbSn units ͑in parentheses͒ for the
crystalline phases of the Sb2S3-Tl2S system. The SbSn units are trigonal pyramids SbS3 ͑tp͒, trigonal bipyra-
mids SbS4 ͑tb͒, and square base pyramids SbS5 ͑sp͒. The values of the Sb coordination numbers and the
Sb-S interatomic distances averaged over the different SbSn units are given by nav and dav͑Sb-S), respec-
tively. The average Tl-S distance is given by dav͑Tl-S).
tp
tb
sp
nav
dav͑Sb-S)
dav͑Tl-S)
Sb2S3
2.53 ͑1͒
2.48 ͑6͒
2.50 ͑2͒
2.70 ͑1͒
2.67 ͑1͒
4
2.62
2.55
2.54
2.60
2.43
TlSb5S8
TlSb3S5
TlSbS2
Tl3SbS3
Tl2S
2.62 ͑3͒
2.61 ͑1͒
2.60 ͑2͒
3.5
3.33
4
3.25
3.17
3.17
3.03
2.87
2.43 ͑1͒
3

56
ELECTRONIC PROPERTIES OF THE CRYSTALLINE . . .
13 057
IV. THEORETICAL APPROACH
terms of the diatomic molecular interactions ss␴, sp␴,
pp␴, and pp␲ obtained by empirical rules. Harrison15 has
proposed a dϪ2 rule, where d is the interatomic distance,
which provides correct electronic structures for covalent ma-
terials when only nearest-neighbor interactions are consid-
ered. Interactions between more distant neighbors decrease
more strongly than expected by a dϪ2 rule and a better
evaluation is obtained by an exponential scaling law as pro-
posed by Robertson.16 Because of the bond-length distribu-
tions in the chalcogenide materials studied in this paper such
an exponential scaling law is used here:
We propose an analysis of the experimental data based on
a tight-binding scheme following the procedure of Slater and
Koster.24 This approach can be easily applied to complex
systems and has been shown to provide correct trends in the
electronic properties of chalcogenide materials.16–18 The
¨
one-electron Schrodinger equation is solved by developing
the wave functions in a basis of Bloch orbitals that are writ-
ten in terms of symmetrically orthogonalized atomic orbitals
͑Lowdin orbitals͒. Because of the orthogonality of these
¨
pseudoatomic orbitals the energy levels E and the wave
functions ⌿ are the eigenvalues and the eigenvectors of the
Hamiltonian matrix, respectively. The dimension of the
Hamiltonian matrix is equal to the total number of atomic
orbitals in the unit cell. A minimal basis set including va-
lence s and p orbitals are considered in the present work.
Thus, the dimension of the matrix is 4Nat , where Nat is the
number of atoms in the unit cell ranging from 16 for TlSbS2
to 81 for Tl2S. The elements of the Hamiltonian matrix can
be written as
ប2
␩
R2␣␤
d␣␤ l͒
͑
ij
hi␣, j␤ l͒ϭ
exp Ϫ␣
Ϫ1
,
͑3͒
͑
ͫ
ͩ
ͪ
ͬ
ij
m
R␣␤
where R␣␤ is the sum of the covalent radii for the atoms
␣ and ␤ as defined by Pauling,22 d␣␤(l) is the distance be-
tween the atoms ␣ and ␤, and ␩ are the Harrison
ij
parameters:26
␩
ϭϪ1.32 eV, ␩ ϭ1.42 eV, ␩ ϭ2.22
ss␴ sp␴ pp␴
eV, ␩ ϭϪ0.63 eV, and ␣ijϭ3. Equation ͑3͒ was used to
pp␲
evaluate the Sb-S and Tl-S interactions with bond lengths
smaller than about 3 and 3.6 Å, respectively. Interactions
between more distant atoms have been neglected because of
their small values.
Hi␣, j␤
ϭ
eik͑R ϩR ϪR hi␣, j␤ l͒
͑1͒
͒
␤
l
␣
͑
͚
l
with
The present analysis of the experimental data requires the
evaluation of the DOS and the atomic charges from the cal-
culated energy levels and wave functions. The partial DOS
*
rϪR ͒H␸ rϪR ϪR ͒,
͑ ͑
␣ j␤ ␤ l
i␣
hi␣, j␤ l͒ϭ
␸
͑2͒
͑
͵
for the orbital ␸ is defined by
i␣
where i, j refer to atomic orbitals (s,px ,py ,pz), R␣ ,R␤ are
the positions in the unit cell of the atoms denoted by ␣ and
␤, respectively, and Rl is the vector of the Bravais lattice
between the unit cells where are located the atoms ␣ and ␤,
respectively. The summation in Eq. ͑1͒ is performed over
several crystal cells because of the strong decrease of
hi␣, j␤(l) with Rl .
Following the idea of Slater and Koster the integrals
hi␣, j␤(l) are not calculated but considered as adjustable
tight-binding parameters. Two types of parameters are usu-
ally distinguished: the intra-atomic parameters that concern
orbitals located on the same atom ͑lϭ1, ␣ϭ␤͒ and the inter-
atomic parameters involving orbitals on different atoms.
As a first approximation, the values of the free-atom en-
ergy can be used for the intra-atomic terms hi␣,i␣(l). How-
ever, large deviations are expected in some cases due to the
ni␣ E͒ϭ
ͦ ␸
͗
͉
⌿
ͦ2␦ EϪE ͒,
͘
͑4͒
͑
͑
͚
i␣
n,k
n,k
n,k
where n and k denote band index and wave vector, respec-
tively. The sum runs over the 4Nat bands for n and a grid of
points in the first Brillouin zone for k. The total DOS is
obtained by summation of the ni␣(E) over all the orbitals
␸
:
i␣
n E͒ϭ
͑
␦ EϪE ͒.
͑5͒
͑
͚
n,k
n,k
The densities of states obtained from Eqs. ͑4͒ and ͑5͒ are
convoluted with a Gaussian of width equal to 1 eV for a
comparison with XPS and XES spectra. The number of elec-
trons i on the atom ␣ can be evaluated by integration of
ni␣(E) over the valence band:
¨
orthogonalization procedure of the Lowdin orbitals as
pointed out previously for oxyde compounds.19 For Sb2S3 a
correct agreement between the XPS spectrum and the calcu-
lated DOS is obtained with the values of the free-atom en-
N ϭ2
i␣
ͦ ␸
͗
͉
␺
ͦ2.
͘
i␣ n,k
͑6͒
ergy
evaluated
by
Hermann
and
Skillman:25
͚
n,k
E3s(S͒ϭϪ20.8 eV, E3p(S͒ϭϪ10.27 eV, E5s(Sb͒ϭϪ14.8
eV, and E5p(Sb͒ϭϪ7.24 eV. For Tl2S the following intra-
atomic energies are used for Tl atoms: E5s(Tl͒ϭϪ13.92 eV
and E5p(Tl͒ϭϪ4.61 eV. The Tl 5s level has been shifted
downwards from the value calculated by Hermann and Skill-
man for a correct agreement between the XPS valence band
and calculated DOS. These intra-atomic parameters that pro-
vide correct DOS for Sb2S3 and Tl2S have been transferred to
the ternary compounds.
Finally, the charge on the atom ␣ is defined as the difference
between the numbers of valence electrons on the free atom
Z␣ and on this atom in the solid:
Q ϭZ Ϫ
N ,
i␣
͑7͒
͚
␣
␣
i
where the summation runs over the valence orbitals ␸ of
the atom ␣.
A two-center approximation is considered for the evalua-
tion of the interatomic terms hi␣, j␤(l), which are written in
i␣

13 058
P. E. LIPPENS et al.
56
FIG. 4. XPS valence band ͑dotted line͒, S K␤ XES spectrum
and calculated DOS for TlSb5S8. The total DOS n(E) and the par-
tial DOS for Sb, Tl, and S atoms are shown. For the partial DOS the
dashed and solid lines correspond to s and p states, respectively.
FIG. 2. XPS valence band ͑dotted line͒, S K␤ XES spectrum,
and calculated DOS for Sb2S3. The total DOS n(E) and the partial
DOS for Sb and S atoms are shown. For the partial DOS the dashed
and solid lines correspond to s and p states, respectively.
V. RESULTS AND DISCUSSION
A. Valence bands
peak for energies greater than Ϫ5 eV labeled II ͑Fig 2͒.
Similar results have been obtained by Leonhardt et al.27
From the partial DOS one can see that the lower-energy part
of the peak I labeled Ia has a strong S 3s character. The
upper energy part Ib has a Sb 5s character due to interactions
between this orbital and the sulfur valence orbitals. The peak
II has a strong S 3p character that results from interactions
between S 3p and Sb 5p orbitals ͑IIa͒ but has also a lone-
pair character ͑IIb͒. The shoulder IIc is due to interactions
between S 3p and Sb 5s orbitals. The XES spectrum shows
a broad and asymmetric band that reflects the S 3p partial
DOS. The main contribution comes from the S 3p lone-pair
states ͑ϷϪ1 eV͒. The asymmetry of the XES band is due to
interactions between S 3p and Sb 5p orbitals ͑ϷϪ4 eV͒.
Because of its strong S 3p character the main peak II of the
XPS spectrum is similar to the XES band.
The XPS valence bands, S K␤ XES spectra and calculated
DOS of the six crystalline phases of the Sb2S3-Tl2S system
are shown in Figs. 2–7. The origin of energies is taken at the
top of the calculated valence bands. Except for Sb2S3 the
XPS valence bands are plotted for energies greater than Ϫ10
eV since the Tl 4d core level at about Ϫ15 eV hides the
lower part of the valence bands. The XPS valence bands are
compared to the total DOS and analyzed from the partial
DOS. The XES spectra are compared to the S 3p partial
DOS.
The valence-band spectrum of Sb2S3 exhibits a broad
band between Ϫ16 and Ϫ6 eV labeled I and an asymmetric
FIG. 3. XPS valence band ͑dotted line͒, S K␤ XES spectrum
and calculated DOS for Tl2S. The total DOS n(E) and the partial
DOS for Tl and S atoms are shown. For the partial DOS the dashed
and solid lines correspond to s and p states, respectively.
FIG. 5. Same as Fig. 4 for TlSb3S5.

56
ELECTRONIC PROPERTIES OF THE CRYSTALLINE . . .
13 059
TABLE III. Binding energies and full widths at half maximum
͑in parentheses͒ of the S 2p3/2 , Tl 4f7/2 , and Sb 4d5/2 core levels
measured by XPS. All values are given in eV.
S 2p3/2
Tl 4f7/2
Sb 4d5/2
Sb2S3
161.3 ͑1.6͒
161.3 ͑1.7͒
161.2 ͑1.6͒
161.1 ͑1.5͒
160.9 ͑1.5͒
160.3 ͑0.7͒
33.1 ͑1.4͒
33.1 ͑1.6͒
33.0 ͑1.5͒
32.9 ͑1.2͒
32.9 ͑1.2͒
TlSb5S8
TlSb3S5
TlSbS2
Tl3SbS3
Tl2S
118.2 ͑1.6͒
118.1 ͑1.4͒
118.1 ͑1.3͒
118.2 ͑1.5͒
117.8 ͑0.9͒
The XPS valence band spectra of the ternary compounds
show an asymmetric and featureless broad band for energies
greater than Ϫ6 eV labeled I ͑Figs. 4–7͒ similar to that ob-
served for Sb2S3 in the same energy range. The width of this
band is found to decrease with increasing Tl2S content. The
XES spectra also show an asymmetric and broad band which
follows the same trend.14 The XES spectrum of Tl3SbS3 ex-
hibits an additional small peak at about Ϫ5 eV and looks like
that of Tl2S whereas the XES spectra of the other ternary
compounds are similar to that of Sb2S3. The partial DOS
show that the main band I of the XPS spectra has a S 3p
character. This band results from interactions between S 3p
and Sb 5p orbitals for energies at about Ϫ3 eV ͑Ia͒ and
exhibits a S 3p nonbonding character for energies at about
Ϫ1 eV ͑Ib͒. We explain the decrease in the widths of the
main XPS and XES peaks from TlSb5S8 to Tl3SbS3 by the
decrease in the amplitude of the DOS structure Ia in relation
with the decrease in the number of Sb-S bonds. The observed
shoulder in the XES spectrum of Tl3SbS3 at about Ϫ5 eV is
attributed to interactions between S 3p and Tl 6s orbitals.
The small influence of the Tl 6s states in the XES spectra of
the other ternary compounds can be explained by the small
values of the Tl-S interactions compared with those of the
Sb-S interactions and by the low value of the ratio ͓Tl͔/͓Sb͔
which varies from 0.2 for TlSb5S8 to 1 for TlSbS2. The ab-
sence of a well-resolved peak in the XPS spectra for the Tl
6s states should be related to the low value of the free-atom
photoemission cross section for these states compared to
those of the other atoms.29
FIG. 6. Same as Fig. 4 for TlSbS2.
The XPS valence-band spectrum of Tl2S is shown in Fig.
3 and is similar to that obtained by Porte et Tranquard.28 The
valence band is formed by two peaks at about Ϫ6 and Ϫ2 eV
labeled I and II, respectively. Peak I has a Tl 6s character
resulting from interactions between Tl 6s and S 3p orbitals.
Peak II has a strong S 3p character due to weak interactions
between S 3p and Tl 6p orbitals ͑IIa͒ and between S 3p and
Tl 6s orbitals ͑IIb͒. The XES spectrum shows a main band at
Ϫ2 eV and a shoulder at about Ϫ6 eV. These two structures
occur at the same energies as the two main peaks I and II of
the XPS spectrum and correspond to the S 3p contribution of
the states involved in these two peaks. It is worth noticing
that the two peaks observed in the XPS valence band have
nearly the same amplitudes whereas the structures of the
XES spectrum have very different intensities since only the
peak II has a strong S 3p character. Finally, the peak due to
the S 3s states, which is predicted at about Ϫ14 eV is not
seen in the XPS spectrum because it is hidden by the Tl 4d
core level.
B. Core levels
The values of the binding energies and the linewidths of
the S 2p3/2 , Tl 4f7/2 , and Sb 4d5/2 core levels measured by
XPS are given in Table III. One can observe a decrease in
the S 2p3/2 binding energy, Eb(S), from Sb2S3 to Tl2S,
which suggests a decrease in the sulfur charge. We have
evaluated the charges Q(S) on the S atoms from Eq. ͑5͒
averaged over the different crystallographic sites. The values
of Q(S) are given in Table IV and a quasilinear correlation
between Eb(S) and Q(S) is obtained ͑Fig. 8͒. In order to
clarify the effect of the Tl atoms upon the S charges another
calculation was carried out which included ionic Tlϩ cations.
This was obtained by neglecting the Tl-S interactions since
the Tl 6s free-atom energy level is located in the valence
FIG. 7. Same as Fig. 4 for Tl3SbS3.

13 060
P. E. LIPPENS et al.
56
TABLE IV. Average values of the Sb 5s, N5s(Sb), S 3s, N3s(S), and Tl 6s, N6s(Tl), numbers of
electrons and average values of the atomic charges Q. The values of the S charges obtained from calculations
including Tl-S interactions, Q(S), or neglecting them, Q (S), are given.
Ј
N
5s(Sb)
Q(Sb)
N3s(S)
Q(S)
Q (S)
Ј
N6s(Tl)
Q(Tl)
Sb2S3
1.9446
1.9380
1.9365
1.9358
1.9250
1.47
1.43
1.45
1.43
1.37
1.959
1.956
1.955
1.953
1.954
1.951
Ϫ0.980
Ϫ0.973
Ϫ0.985
Ϫ1.015
Ϫ1.091
Ϫ1.213
Ϫ0.980
Ϫ1.013
Ϫ1.056
Ϫ1.191
Ϫ1.431
Ϫ2
TlSb5S8
TlSb3S5
TlSbS2
Tl3SbS3
Tl2S
1.992
1.988
1.990
1.991
1.991
0.63
0.58
0.60
0.63
0.62
Sb. Thus, the contributions of the different crystallographic
sites occupied by the Sb atoms cannot be detected and only
one site has been considered in the fitting procedure of the
spectra.
The values of the isomer shift ␦, the quadrupole splitting
⌬, and the linewidth ⌫ are given in Table V. The values of ⌬
are found in the range 10.8–12.7 mm/s suggesting a strong
anisotropy of the Sb local environments in agreement with
the structural description ͑Table II͒. The low value of ⌫ for
Tl3SbS3 ͑1.2 mm/s͒ compared with the values obtained for
the other antimony compounds ͑1.4–1.7 mm/s͒ is consistent
with the existence of only one crystallographic site for the Sb
band and the Tl 6p free-atom energy level in the conduction
band. The results also show a decrease of the charges Q(S)
Ј
from Sb2S3 to Tl2S ͑Fig. 8͒. Significant quantitative differ-
ences with the previous calculation is observed especially for
Tl3SbS3 and TlSbS2. The charges on the Tl atoms decrease
when Tl-S interactions are taken into account leading to an
increase of the S charges by an amount of about 0.35͓Tl͔/͓S͔,
where the brackets denote the atomic concentrations. Al-
though the Tl atoms strongly influence the S charges it is
worth noticing that both calculations predict the correct
trends in the variations of Eb(S). In addition, these two cal-
culations provide similar values for the Sb charges indicating
that Tl-S interactions have negligible effects on the elec-
tronic population of this atom. The values of the Tl 4f7/2 and
Sb 4d5/2 binding energies ͑Table III͒ do not vary noticeably
and are found within experimental errors ͑Ϯ0.1 eV͒ except
for the Tl 4f7/2 binding energy of Tl2S, which is slightly
lower ͑0.3 eV͒ than the other values. The absence of signifi-
cant variations could be explained from the small changes in
the calculated atomic charges ͑Ͻ0.1͒ and because Sb and Tl
are heavy atoms.
atoms in Tl3SbS3.
121
¨
Sb Mossbauer isomer shift ␦ are
The values of the
characteristic of Sb3ϩ cations30 as proposed from a previous
structural analysis.12 They are found to increase from Sb2S3
͑Ϫ6.03 mm/s͒ to Tl3SbS3 ͑Ϫ3.14 mm/s͒. In order to analyze
the evolution of ␦ we consider the usual expression,30
␦ϭ␣nuc
␳
0͒Ϫ␳ 0͒ ,
͑8͒
͓
͑
͑
͔
a
s
where ␣nuc is a nuclear constant, ␳ and ␳ are the electron
a
s
densities at the nucleus in the absorber and in the source,
respectively. The nuclear constant ␣nuc is a function of the
relative change in the radius of the nuclear states involved,
⌬R/R, which is negative for Sb.30 Thus, the observed in-
121
¨
C. Sb Mossbauer spectroscopy
121
¨
Sb Mossbauer spectrum is shown in Fig. 9
A typical
for TlSb5S8 and rather similar spectra are obtained for the
other antimony compounds. They all exhibit a broad band
͑Ϸ10 mm/s͒ due to the eight allowed nuclear transitions for
FIG. 8. Correlations between the experimental values of the S
2p3/2 core-level binding energy and the charges on S calculated
with Tl-S interactions ͑squares͒ and without Tl-S interactions
͑circles͒. 1, Sb2S3; 2, TlSb5S8; 3, TlSb3S5; 4, TlSbS2; 5, Tl3SbS3; 6,
Tl2S.
121
¨
Sb Mossbauer spectrum of TlSb5S8. The velocity
FIG. 9.
scale is referenced to InSb material.

56
ELECTRONIC PROPERTIES OF THE CRYSTALLINE . . .
Sb Mossbauer parameters relative to InSb. Values
13 061
121
¨
TABLE V.
¨
of the Mossbauer isomer shift ␦, the quadrupole splitting ⌬, and the
full width at half maximum ⌫ are given in mm/s.
␦
⌬
⌫
Sb2S3
Ϫ6.03
Ϫ5.09
Ϫ4.57
Ϫ4.26
Ϫ3.14
10.8
12.0
12.5
12.7
11.1
1.42
1.55
1.70
1.61
1.19
TlSb5S8
TlSb3S5
TlSbS2
Tl3SbS3
crease of ␦ from Sb2S3 to Tl3SbS3 suggests a decrease of
␳a(0). An accurate evaluation of the electronic density at the
nucleus is rather difficult for solids with complex structures.
However, variations of ␳a(0) are mainly dependent on
changes in the number of Sb 5s electrons, N5s(Sb), and to a
lesser extent on changes in the number of Sb 5p electrons,
FIG. 11. Variations of the surface of the first XAS peak at the
LIII edge of Sb ͑in arbitrary units͒ as a function of the calculated
number of Sb 5s electrons Ns(Sb). The straight line is obtained by
linear regression. The numbering is the same as in Fig. 8.
2n5s,Sb(E) over the conduction band gives 2-N5s(Sb). We
assume that the transition probability between the Sb 2p3/2
core level and the Sb 5s empty states does not vary notice-
ably with energy. This means that the surface of the observed
XAS peak should vary as 2-N5s(Sb). We have evaluated the
surface Sp of this peak from the XAS spectra by considering
as boundary values: Spϭ0 for Sb2S3 and Spϭ1 for Tl3SbS3.
As expected, a linear correlation between the values of Sp
N
5p(Sb). As a first approximation ␳a(0) is expected to vary
linearly with N5s(Sb).18 The tight-binding calculations give
N5s(Sb)Ϸ2 for the different antimony compounds but a
small decrease of N5s(Sb) from Sb2S3 to Tl3SbS3 is obtained
͑Table IV͒. The observed linear correlation between the ex-
perimental values of ␦ and the calculated values of N5s(Sb)
confirms the main influence of the Sb 5s electrons on the
¨
Mossbauer isomer shift ͑Fig. 10͒.
and the calculated values of N5s(Sb) is found ͑Fig. 11͒.
121
¨
Since the Sb Mossbauer isomer shift ␦ varies linearly with
D. X-ray absorption spectroscopy
N5s(Sb), a linear correlation between Sp and ␦ is obtained
that can be explained by the strong influence of the Sb 5s
electrons upon these two experimental parameters ͑Fig. 12͒.
The XAS at the Sb LIII edge has been recently used to
investigate the local structure in the crystalline and glassy
phases of the Sb2S3-As2S3-Tl2S system.13 The electronic
transitions from the inner Sb 2p3/2 core level to the Sb empty
states that obey selection rules ͑s-type and d-type final
states͒ were concerned. The spectra clearly exhibit a peak at
about 4137 eV whose the amplitude increases from Sb2S3 to
Tl3SbS3. This peak occurs at the absorption edge and can be
attributed to the empty Sb 5s states localized at the bottom
of the conduction band.
These results show that the combined application of XAS
121
¨
and Sb Mossbauer spectroscopy provides very interesting
information for the study of antimony compounds.
VI. LOCAL ELECTRONIC STRUCTURES
A. Sb atoms
In the preceding section it has been shown that tight-
binding calculations provide a correct analysis of the experi-
mental electronic structures of the crystalline phases of the
Sb2S3-Tl2S system. The experimental results obtained by
The number of Sb 5s electrons, N5s(Sb), is obtained by
integration over the valence band of the partial DOS includ-
ing the spin degeneracy 2n5s,Sb(E). Thus, integration of
¨
XPS ͑core levels͒, XAS, and Mossbauer spectroscopy have
121
¨
FIG. 10. Variations of the experimental Sb Mossbauer isomer
shift ␦ as a function of the calculated number of Sb 5s electrons
Ns(Sb). The straight line is obtained by linear regression. The num-
bering is the same as in Fig. 8.
FIG. 12. Linear correlation between the surface of the first XAS
121
¨
peak at the LIII edge of Sb ͑in arbitrary units͒ and the Sb Moss-
bauer isomer shift. The numbering is the same as in Fig. 8.

13 062
P. E. LIPPENS et al.
56
been correlated to the calculated numbers of electrons. In this
section, we propose simple molecular calculations in order to
relate the electronic populations to the local atomic environ-
ments by simple analytical expressions.
E5p Sb͒ϪE S͒
͑
͑
3p
␥ϭ
,
͑12͒
2␤
where E5p(Sb) and E3p(S) are the intra-atomic energies and
␤ denotes the pp␴ interaction between Sb and S atoms as
defined by Eq. ͑3͒. Following the idea of Harrison15 concern-
ing sp3 covalent semiconductors, the term ␣Ј given by Eq.
͑11͒ can be viewed as the Sb-S bond polarity neglecting the
effects of the s orbitals. The term ␥ is the ratio between the
heteropolar term E5p(Sb)-E3p(S) and the homopolar term
2␤, which can both be compared to the two parts of the
average band gap as defined by Phillips.31 This can be
viewed as a measure of the ionocovalent character of the
Sb-S bond. Depending on the value of ␥ the polarity ␣Ј
varies between Ϫ1 and ϩ1. These two values of ␣Ј corre-
spond to complete electronic transfers ͑ionic bonds͒ whereas
for ␣ϭ0 the bond is covalent. For the Sb-S bonds found in
the SbSn molecules the polarity is of about 0.5.
We first describe the approximations used for the molecu-
lar calculations of the electronic populations on Sb atoms.
First, we only consider the dominant pp␴ interactions be-
tween Sb and S nearest neighbors. The other molecular in-
teractions (ss␴,sp␴,pp␲) and the pp␴ interactions be-
tween the other pairs of atoms are neglected. Second, we
take the Sb-S-Sb angles equal to 90°. In this case, the S
atoms have less than three Sb nearest neighbors in orthogo-
nal directions and there are only interactions between Sb 5p
orbitals and combinations of S 3p orbitals pointing towards
the Sb atoms. With these two approximations the crystals
behave as a set of isolated SbSn units with negative charges
and Tlϩ ions. The electronic structures of the ternary phases
are formed by the molecular levels of the SbSn units and the
atomic levels of Tlϩ. The main effect of the other interac-
tions is to broaden these levels into bands as obtained from
the tight-binding calculations of Sec. V.
In the same way, we can evaluate the contribution of the
S-Sb-S molecules to the number of Sb 5p electrons:
As shown by Eq. ͑6͒ the number of electrons Ni␣ is ob-
tained from the projection of the electronic wave functions
onto the atomic orbital ␸i␣ . Since there are no interactions
involving the Sb 5s orbitals in the present molecular model
we have N5s(Sb)ϭ2. The evaluation of N5p(Sb) requires the
calculation of the wave functions for the SbSn molecules. In
order to obtain a simple analytical expression for N5p(Sb)
the S-Sb-S angles that are found in the range 76°–108° are
taken to be equal to 90°. In this case the SbSn units can be
described by (6Ϫn) Sb-S diatomic molecules and (nϪ3)
S-Sb-S linear molecules. There are no interactions between
these molecules which are found in three orthogonal direc-
tions. The analytical expressions of the energy levels and
wave functions can be easily derived for these simple mol-
ecules. The electronic structure of a Sb-S molecule is formed
by a pair of bonding/antibonding states resulting from inter-
actions between S 3p and Sb 5p orbitals. The electronic
structure of a S-Sb-S molecule is formed by a nonbonding S
3p state and a pair of bonding/antibonding states arising
from interactions between Sb 5p orbitals and a combination
of 3p orbitals of the two S atoms. The number of Sb 5p
electrons is obtained from the Sb 5p contribution of the
bonding states since they are always found in the valence
band. We consider for simplicity that all the Sb-S bond
lengths within a SbSn molecule are equal to the average
value d. In this case N5p(Sb) can be evaluated from the
contributions of the Sb 5p electrons of the Sb-S molecules,
N5p͑Sb͒ ϭ1Ϫ␣
͑13͒
Љ
Љ
with
␥
␣ ϭ
Љ
,
͑14͒
2
ͱ
2ϩ␥
where ␥ is defined by Eq. ͑12͒. The coefficient ␣Љ can also be
defined as a polarity coefficient but for the electronic tranfer
between the central Sb atom and the two S atoms of the
S-Sb-S molecule. This coefficient varies from 0.4 to 0.6 as
the Sb-S distance increases from 2.5 to 3 Å.
The number of Sb 5p electrons can be written in terms of
the polarity coefficients ␣Ј and ␣Љ from Eqs. ͑9͒, ͑10͒, and
͑13͒:
N5p Sb͒ϭ3ϩ3 ␣ Ϫ2␣ ͒ϩn ␣ Ϫ␣ ͒.
͑15͒
͑
͑
͑
Ј
Љ
Ј
Љ
Putting the expressions ͑11͒, ͑12͒, and ͑14͒ in Eq. ͑15͒ yields
an analytical but rather complex expression for N5p(Sb) in
terms of the Sb coordination, the average Sb-S bond length
and the free-atom energy values of Sb and S. This expression
can be simplified by considering the small variations of the
average Sb-S bond length d within each SbSn unit ͑Table II͒.
The expressions ͑11͒ and ͑14͒ of the bond polarities are ex-
panded in Taylor series around d0ϭ2.4 Å ͑sum of the Sb and
S covalent radii͒ in terms of ⌬dϭdϪd0 . This gives for Eq.
͑15͒
N5p(Sb) , and of the S-Sb-S molecules, N (Sb) . This
Ј
Љ
5p
gives
N5p Sb͒Ϸ1.28Ϫ1.58⌬dϩn 0.12ϩ0.08⌬d͒. ͑16͒
͑
͑
N5p Sb͒ϭ 6Ϫn͒N Sb͒ ϩ nϪ3͒N Sb͒ .
͑9͒
͑
͑
͑
͑
͑
Ј
Љ
5p
5p
The second and third terms of the right side of this equation
have opposite signs. Since d increases by about 0.3 Å as n
increases from 3 to 5 ͑Table II͒ these two terms tend to
cancel each other. Evaluation of Eq. ͑16͒ for the different
SbSn units of the antimony compounds gives N5p(Sb)ϭ1.6
Ϯ0.1. Thus, the values of the Sb charges, Q(Sb)Ϸ1.4, are in
close agreement with those obtained by the tight-binding cal-
culations of Sec. V ͑Table IV͒. This simple molecular model
shows that charges on Sb do not vary noticeably for the
The contribution of the diatomic molecules to the number of
Sb 5p electrons is given by
N5p Sb͒ ϭ1Ϫ␣
͑10͒
͑11͒
͑
Ј
Ј
with
␥
␣ ϭ
Ј
,
2
ͱ
1ϩ␥

56
ELECTRONIC PROPERTIES OF THE CRYSTALLINE . . .
13 063
different compounds studied in this paper. This can be cor-
related with the absence of significant variations for the Sb
4d5/2 binding energy.
ably to N (Sb) ,which mainly depends on the contributions
of the diatomic molecules. By using Eq. ͑17͒ for the Sb-S
molecules one obtains
Ј
5s
The preceding molecular model predicts a population of
two 5s electrons on Sb, independently of the Sb coordination
because interactions involving the Sb 5s orbitals have been
neglected. The tight-binding calculations of Sec. V have
given similar results although a small decrease of N5s(Sb)
from Sb2S3 to Tl3SbS3 has been found and correlated to the
a2⌬2
2ϪN5s Sb͒ Ϸ
.
͑19͒
͑
Ј
2
E ϪE Sb͒
͔
͓
͑
a
5s
We use Eq. ͑3͒ for ⌬ and values of the tight-binding param-
eters given in Sec. IV. The term a/ E ϪE (Sb) does not
͓
͔
a
5s
vary noticeably with the Sb-S bond length and can be ex-
panded in Taylor series at first order in ⌬dϭdϪd0 . This
gives for Eq. ͑19͒
¨
observed increase of the Mossbauer isomer shift ␦. In order
to clarify the influence of the local structural changes around
the Sb atoms onto the variations of ␦ an analytical expression
of N5s(Sb) is derived. Following the idea of Lefebvre et al.18
we propose an evaluation of N5s(Sb) for the Sb atoms of the
SbSn molecules from a simple perturbation theory.
2ϪN5s Sb͒ Ϸ 0.024Ϫ0.013⌬d͒eϪ2.5⌬d
.
͑20͒
͑
͑
Ј
The number of Sb 5s electrons for a SbSn molecule,
N5s(Sb), is obtained from the contributions of the (6Ϫn)
Sb-S molecules given by Eq. ͑20͒. For simplicity we con-
sider that all the Sb-S interatomic distances within a SbSn
molecule have the same average value d since they do not
vary by more than 0.15 Å. The number of Sb 5s electrons is
given by
Let us first calculate the number of Sb 5s electrons,
N (Sb) , in a S -Sb-S linear asymmetric molecule. The
Ј
5s
1
2
pp␴ interactions are written ␤1 ,␤2 and the sp␴ interactions
⌬1 ,⌬2 , where the indices 1 and 2 denote the Sb-S1 and
Sb-S2 bonds, respectively. The zeroth-order approximation
to the molecular wave functions is obtained from the preced-
ing molecular model. The sp␴ interactions are introduced by
an evaluation of the molecular wave functions at first order.
We obtain
N5s Sb͒Ϸ2Ϫ 6Ϫn͒ 0.056Ϫ0.013d͒eϪ2.5dϩ6
.
͑21͒
͑
͑
͑
This expression shows that increases in the Sb coordination
number n and in the Sb-S bond length d both tend to de-
crease N5s(Sb). In addition, N5s(Sb) is strongly dependent
on the Sb coordination number n which varies from 3 to 5
and to a lesser extent on the average Sb-S bond length d,
which varies by less than 0.15 Å. Considering for simplicity
that dϭ2.5 Å, we obtain
2
a2
E ϪE Sb͒
͔
␤ ⌬ Ϫ␤ ⌬ ͒
1 1 2 2
͑
N5s Sb͒ ϭ2Ϫ
͑17͒
͑
Ј
2
2
␤
͓
͑
5s
a
with
1/2
1ϩ␥2Ϫ␥ ␥2ϩ1͒
a2ϭ1Ϫ
,
1/2
N5s Sb͒Ϸ1.890ϩ0.018n.
͑22͒
͑
͑
For a crystal, the number of Sb 5s electrons is obtained by
averaging the values of N5s(Sb) obtained by Eq. ͑22͒ over
the different Sb sites. This gives the same expression as Eq.
͑22͒ but with the average Sb coordination number nav given
in Table II instead of n. From Sb2S3 to Tl3SbS3 nav is found
to decrease from 4 to 3 leading to a decrease of N5s(Sb)
from 1.962 to 1.946. These values are greater than those
obtained from the tight-binding calculations of Sec. V ͑Table
IV͒ by about 0.02 electron but the same trend is observed
except for TlSbS2, which has the same average coordination
as Sb2S3. This can be due to the simplicity of the present
molecular model. However, this calculation clearly shows
1/2
EaϭE5p Sb͒Ϫ␤␥ϩ␤ ␥2ϩ1͒
,
͑
͑
E5p Sb͒ϪE S͒
͑
͑
3p
␥ϭ
,
2␤
␤2ϭ␤21ϩ␤22.
Considering the exponential bond-length dependence of the
hopping integrals ⌬ and ␤ given by Eq. ͑3͒, it can be shown
that a/ E ϪE (Sb) varies slightly with the Sb-S bond
͓
͔
a
5s
length d and that
¨
that the observed main trends in the variations of the Moss-
͒/d
0
2ϪN5s Sb͒ ϳ1Ϫe6͑d Ϫd
,
͑18͒
1
2
͑
Ј
bauer isomer shift and the surface of the first XAS peak,
which both strongly depend on N5s(Sb), can be roughly ex-
plained by the changes in the Sb coordination number.
where d1 and d2 are the bond lengths of the Sb-S1 and Sb-S2
molecules, respectively, and d0ϭ2.4 Å is the sum of the Sb
and S covalent radii. For d1ϭd2 Eq. ͑18͒ shows that
B. S atoms
N (Sb) is equal to 2, indicating that in this case the
Ј
5s
S1-Sb-S2 molecules do not contribute to changes in
It has been shown in Sec. V that the S 2p3/2 binding
energy decreases from Sb2S3 to Tl2S consistently with the
decrease of the average sulfur charges evaluated by tight-
binding calculations ͑including or not including Tl-S interac-
tions͒. In order to relate these changes to the local environ-
ments of the S atoms, we propose a molecular calculation
with the same basic approximations as in Sec. VI A. We only
consider pp␴ interactions between S and Sb nearest neigh-
bors and the Sb-S-Sb angles are taken to be equal to 90°.
Interactions with Tl atoms are neglected and these atoms are
N (Sb) . For d Þd the contribution of the S -Sb-S mol-
Ј
5s
1
2
1
2
ecules to 2-N (Sb) increases with the asymmetry of the
Ј
5s
molecules. If the difference between d1 and d2 is greater
than about 1 Å the influence of the most distant S atom can
be neglected and the molecule is equivalent to a diatomic
molecule. For distances smaller than 1 Å the contribution of
the asymmetric S1-Sb-S2 molecules is found to be always
smaller than that of the Sb-S molecules of the same SbSn
unit. Thus, the S1-Sb-S2 molecules do not contribute notice-

13 064
P. E. LIPPENS et al.
56
S-Sb molecules, N (S) , and of the n S-Sb-S molecules,
Ј
Ј
3s
N3p(S) , and from the contribution of the S 3p electrons to
Љ
the nonbonding states: 6Ϫ2n. If we consider for simplicity
that all the Sb-S bond lengths within a SSbnSn molecule
Ј
have the same average bond length d, we obtain
N3p S͒ϭ6Ϫ2nϩ nϪn ͒N S͒ ϩn N S͒ ͑23͒
͑
͑
͑
͑
Ј
Ј
Ј
Љ
3p
3p
with
N3p S͒ ϭ1ϩ␣ ,
͑24͒
͑25͒
͑
Ј
Ј
1
N3p S͒ ϭ2Ϫ
,
͑
Љ
2ϩ␥2ϩ␥ ␥2ϩ2͒
1/2
͑
FIG. 13. Schematic description of the local environments of the
S atoms for the crystalline phases of the Sb2S3-Tl2S system. The
where ␣Ј and ␥ are given by Eqs. ͑11͒ and ͑12͒, respectively.
As for the SbSn units, we expand Eqs. ͑24͒ and ͑25͒ in Tay-
lor series around d0ϭ2.4 Å in terms of ⌬dϭdϪd0 , which
depends on the environment of the S atoms ͑Table VI͒. The
resulting first-order approximation to Eq. ͑23͒ reads
molecules are of the form SSbnSn with nр3 and n рn. Only, the
Ј
Ј
SSb3S3 molecule is shown for clarity. The other SSbnSn molecules
Ј
may be drawn from this figure by eliminating (3Ϫn) Sb and
(3Ϫn ) S atoms.
Ј
assumed to be ionic (Tlϩ). This approximation has a notice-
able effect on the values of the S charges but not on their
variations as shown in Sec. V. Since there are no interactions
with the S 3s orbitals in the present model the S atoms have
two 3s electrons in correct agreement with the tight-binding
calculations of Sec. V, which give N5s(S)Ϸ1.96 electron for
the different compositions ͑Table IV͒. This can be explained
by the deep S 3s atomic level compared with the values of
the other atomic levels involved in calculations. The evalua-
tion of the number of S 3p electrons, N3p(S), requires the
determination of the molecules describing the S local envi-
ronments. The S atoms are surrounded by less than three Sb
nearest neighbors. Because the Sb coordination number is
greater or equal to 3 the other S atoms included in linear
S-Sb-S molecules have to be taken into account. Thus, the
N3p S͒Ϸ6Ϫn 0.54Ϫ0.45⌬d͒ϩn 0.21Ϫ0.26⌬d͒.
͑
͑
͑
Ј
͑26͒
This expression shows that the number of S 3p electrons
increases slightly with the average bond length ͑because
⌬dϭ0Ϫ0.3 Å͒ and decreases with the S coordination num-
ber n and the number of S-Sb-S molecules n . The average
Ј
number of S 3p electrons in a crystal is obtained by summa-
tion of the N3p(S) over the different S environments given in
Table VI. By neglecting the variations of d over the different
SSbnSn units of a crystal we obtain the same expression as
Ј
Eq. ͑26͒ but with the average values nav ,naЈv and ⌬davϭdav
Ϫd instead of n,n and ⌬d, respectively. These values as
Ј
0
well as the calculated values of the average S charges,
Qav͑S), are given in Table VI. Comparison between the S
molecules are of the form SSbnSn , where nр3 is the S
charges, Q (S), obtained by the tight-binding calculations of
Ј
Ј
coordination number and n рn is the number of linear S-
Ј
Sec. V without Tl-S interactions ͑Table IV͒ and Qav͑S)
shows a good agreement ͑Ͻ0.1 electron͒. Thus, molecular
and tight-binding calculations provide similar variations of
the S charges which are consistent with the variations of the
S 2p3/2 binding energy. The present molecular calculation
shows that the observed decrease in the S 2p3/2 binding en-
ergy from Sb2S3 to Tl2S can be explained by the decrease in
the average S coordination number nav which is the leading
parameter in Eq. ͑26͒. However, it is clear that the partial
covalent character of the Tl-S bonds, which are not taken
into account in this simple model, tends to reduce this effect
as shown in Sec. V.
Sb-S molecules. A schematic description is given in Fig. 13
and the different S environments found in the materials stud-
ied in this paper are reported in Table VI. Because all the
bond angles are assumed to be proportional to 90°, there are
no interactions between the SSbnSn molecules. In addition,
Ј
the SSbnSn molecules are formed by n linear S-Sb-S mol-
Ј
Ј
ecules and (nϪn ) S-Sb molecules in three orthogonal di-
Ј
rections. The electronic structure of the SSbnSn molecules is
Ј
formed by the molecular levels of the noninteracting S-Sb
and S-Sb-S molecules. Thus, N3p(S) can be evaluated from
the S 3p contributions to the bonding states of the (nϪn )
Ј
TABLE VI. Structural information for the molecular calculation of the charge on S: Qav͑S). The average
Sb-S interatomic distances ͑in Å͒ and the numbers of SSbnSn molecules ͑in parentheses͒ are given for the
Ј
different crystalline phases. The values of the Sb-S interatomic distances, n and n averaged over the
Ј
different SSbnSn units are given by dav , nav , and nЈ , respectively.
av
Ј
SSb1S0
SSb2S0
SSb2S1
SSb3S1
SSb3S2
dav
nav
Qav͑S)
nav
Ј
Sb2S3
2.46 ͑1͒
2.49 ͑8͒
2.52 ͑3͒
2.71 ͑2͒
2.70 ͑2͒
2.63
2.57
2.57
2.66
2.44
2.67
2.19
2
2
1
1.33
0.63
0.45
1
Ϫ1.03
Ϫ1.09
Ϫ1.14
Ϫ1.30
Ϫ1.48
TlSb5S8
TlSb3S5
TlSbS2
Tl3SbS3
2.63 ͑5͒
2.64 ͑2͒
2.66 ͑4͒
2.64 ͑1͒
2.44 ͑1͒
0

56
ELECTRONIC PROPERTIES OF THE CRYSTALLINE . . .
13 065
VII. CONCLUSIONS
Sb2S3 to Tl3SbS3 have been explained from the decrease of
the Sb coordination number. The variations of the Sb 4d5/2
binding energy have been found to be very small because of
the opposite influences of the Sb coordination number and
the Sb-S bond lengths. The observed decrease in the S 2p3/2
binding energy from Sb2S3 to Tl3SbS3 has been related to the
decrease of the average S coordination number. Thus, tight-
binding calculations and molecular models provide a coher-
ent picture of the observed main trends in the variations of
the electronic properties of the crystalline phases of the
Sb2S3-Tl2S system.
The electronic properties of the crystalline phases of the
¨
Sb2S3-Tl2S system have been studied by XPS and Mossbauer
spectroscopies. These results as well as previous results ob-
tained by S K␤ XES and XAS have been explained from
tight-binding calculations that take into account the real and
complex structure of the materials. The main features of the
XPS valence bands and XES spectra have been analyzed in
terms of atomic orbital contributions. The variations of the
121
¨
XPS core levels, the
Sb Mossbauer isomer shift and the
XAS prepeak surface have been correlated to changes in the
calculated numbers of valence electrons. It has been shown
121
¨
that the Sb Mossbauer isomer shift and the surface of the
ACKNOWLEDGMENTS
XAS prepeak at the Sb LIII edge can be linearly correlated
because they both strongly depend on the number of Sb 5s
electrons. Simple molecular models have been proposed to
relate the experimental data to the local structure. The ob-
The research was performed under a European Research
Network Programme ͑GDRE͒ ‘‘Chalcogenides’’ initiated by
the Centre National de la Recherche Scientifique ͑France͒.
We also acknowledge the support of the Centre National
Universitaire Sud de Calcul ͑France͒.
121
¨
served increases in the
Sb Mossbauer isomer shift and in
the surface of the XAS prepeak at the Sb LIII edge from
*
Electronic address: lippens@chalco.univ-montp2.fr
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