Electronic structure, galvanomagnetic and magnetic properties of the bismuth subhalides Bi4I4 and Bi4Br4

Article abstract of DOI:10.1016/j.jssc.2007.01.010

Two bismuth-rich subhalides, Bi₄Br₄ and Bi₄I₄, featuring extended quasi one-dimensional metallic fragments in their structures, have been investigated. The gas-phase technique of crystal growth has been refined for obtaining large (up to 5 mm long) single crystals. Electronic structure calculations on three-dimensional structures of both compounds have been performed (DFT level, hybrid B3LYP functional), predicting a semiconducting behavior for both compounds, with an indication of possible directional anisotropy of electric conductivity. Galvanomagnetic (resistance, magnetoresistance, Hall effect, thermopower) and magnetic (temperature and field dependence of magnetization) properties have been measured experimentally. Both compounds are found to be diamagnetic, room-temperature semiconductors with n-type conductivity. While Bi₄Br₄ demonstrates a typical case of one dimensionality, the difference in magnetoresistivity between Bi₄Br₄ and Bi₄I₄ indicates some weak interactions between isolated bismuth metallic fragments within the bismuth substructures.

Full text of DOI:10.1016/j.jssc.2007.01.010

ARTICLE IN PRESS
Journal of Solid State Chemistry 180 (2007) 1103–1109
www.elsevier.com/locate/jssc
Electronic structure, galvanomagnetic and magnetic properties of the
bismuth subhalides Bi4I4 and Bi4Br4
Ã
T.G. Filatovaa, P.V. Gurinb, L. Klooc, V.A. Kulbachinskiib, A.N. Kuznetsova, , V.G. Kytinb,
M. Lindsjoc, B.A. Popovkina
aDepartment of Chemistry, Moscow State University, 119992 Leninskie Gory 1-3, GSP-2, Moscow, Russian Federation
bDepartment of Physics, Moscow State University, 119992 Leninskie Gory 1-2, GSP-2, Moscow, Russian Federation
cDepartment of Chemistry, Royal Institute of Technology, S-100 44 Stockholm, Sweden
Received 23 October 2006; received in revised form 27 December 2006; accepted 5 January 2007
Available online 20 January 2007
Abstract
Two bismuth-rich subhalides, Bi4Br4 and Bi4I4, featuring extended quasi one-dimensional metallic fragments in their structures, have
been investigated. The gas-phase technique of crystal growth has been refined for obtaining large (up to 5 mm long) single crystals.
Electronic structure calculations on three-dimensional structures of both compounds have been performed (DFT level, hybrid B3LYP
functional), predicting a semiconducting behavior for both compounds, with an indication of possible directional anisotropy of electric
conductivity. Galvanomagnetic (resistance, magnetoresistance, Hall effect, thermopower) and magnetic (temperature and field
dependence of magnetization) properties have been measured experimentally. Both compounds are found to be diamagnetic, room-
temperature semiconductors with n-type conductivity. While Bi4Br4 demonstrates a typical case of one dimensionality, the difference in
magnetoresistivity between Bi4Br4 and Bi4I4 indicates some weak interactions between isolated bismuth metallic fragments within the
bismuth substructures.
r 2007 Published by Elsevier Inc.
Keywords: Bismuth-rich compounds; Subhalides; Low-dimensional structures; Electronic structure; Conductivity; Magnetic properties
1. Introduction
One-dimensional polymer molecules in the compounds
in question are stacked into two-dimensional fragments
that, in turn, are parallel to each other and comprise a
three-dimensional molecular crystal lattice. Since, as is
evident from the respective interatomic distances [11],
molecules and stacks are rather weakly bonded to each
other, the crystals are expected to be highly anisotropic.
While the crystal structures of such compounds have been
extensively studied over the years, data on their electrical
and magnetic properties are very scarce.
According to Ref. [6], bismuth monoiodide crystallizes in
three different modifications; two of them, a- and b-Bi4I4,
have been structurally characterized and differ only
slightly in the way of stacking of the polymeric entities.
The structure of bismuth monobromide [4] is highly
related to the both monoiodide modifications. All
three phases crystallize in the monoclinic space group
C2/m. The fragment of Bi4Br4 structure is shown in
Fig. 1.
A small number of different bismuth subhalides have
been reported in literature. Their crystal structures feature
either bismuth cluster polycations Bi59+: BiCl1.167 [1,2],
Bi7Cl19 [3], and BiBr1.167 [4], or extended one-dimensional
polymer molecules formed by corrugated bismuth stripes
or ribbons of varying width, terminated from two sides by
halogen atoms. Such four atom-wide ribbons were found in
the structures of Bi4Br4 [4], Bi4I4 [5–7], Bi4BrI3, Bi4Br2I2,
and Bi4Br3I [8], and 14 and 18 atom-wide ribbons
were found in Bi14I4 [9] and Bi18I4 [10], respectively. The
geometry of bismuth–bismuth bonds within a single
polymer molecule in such subhalides and the two-dimen-
sional corrugated layer present in the structure of bismuth
metal is almost identical.
Ã
Corresponding author. Fax: +7 495 9390998.
E-mail address: alexei@inorg.chem.msu.ru (A.N. Kuznetsov).
0022-4596/$ - see front matter r 2007 Published by Elsevier Inc.
doi:10.1016/j.jssc.2007.01.010

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Hg2Br2 were used as starting materials. Bismuth to
mercury halide molar ratios in different experiments were
either 4:1 or 2:1, with a total amount of approximately 2 g.
Silica ampoules with the length of 20–25 cm and
inner diameter of 10 or 15 mm were used for crystal
growth. The duration of the experiments varied from 24 to
72 h. Ampoules were dried under dynamic vacuum (ca.
0.01 Torr) prior to their use, then one end was filled with
the reaction mixture, and the ampoules were flame-sealed
under vacuum and placed into a slightly tilted horizontal
two-temperature furnace in such a way that the hotter end
containing the mixture was in a lower position than the
empty colder one. Two combinations of cold/hot end
temperatures were used: 165/275 and 200/278 1C.
Single crystals of Bi4I4 were obtained as black needles or
as elongated flexible platelets. The shape of the crystals was
primarily dependent of the inner diameter of the ampoules
used. Bundles of multiple needle-like crystals up to 1 mm
long were obtained on the walls of the ampoules with
15 mm inner diameter at 200–250 1C temperatures. When
using ampoules with a smaller inner diameter (10 mm), we
observed the formation of platelets and needles up to 5 mm
long in the temperature zone around and over the mixture.
According to X-ray powder diffraction (XRPD) data
(CuKa1 radiation, Guinier camera FR-552, Enraf-Nonius),
both types of crystals were b-Bi4I4 [6], and according to
EDX data (CAMEBAX SX-50) atomic percentages of
bismuth and iodine, averaged over 3 points, were 49.4 and
49.7, respectively, which are within the margin of error (ca.
1 at%) to the Bi4I4 formula. XRPD data also indicated that
bismuth metal and Bi14I4 were always present in the bulk
after the reaction. In all cases a pinkish substance was
visible in the cold end of the ampoules. This compound was
identified as Hg2I2.
Single crystals of Bi4Br4 were obtained as black needles
up to 2 mm in length or very thin flexible platelets up to
3 mm in length and 0.5 mm in width on the walls of the
ampoules in the 210–230 1C temperature zone. The
composition of the crystals was confirmed by XRPD and
EDX analyses (average bismuth and bromine content
was 49.1 and 50.4 at%, respectively). According to
XRPD data, the rest of the bulk contained bismuth
metal, as well as visible droplets of mercury. It should be
noted that our attempts to follow the authors of Ref. [4]
and obtain Bi4Br4 crystals from the mixture of Bi and
HgBr2 (3:1 molar ratio and total amount of approximately
2 g; heating the reaction ampoules for 3 days in the
temperature gradient 200/270 1C) were unsuccessful.
A microcrystalline substance was observed to have formed
in the 200–250 1C zone; using XRPD analysis it was
identified as BiBr3.
Fig. 1. A fragment of Bi4Br4 structure, showing the spatial arrangement
of the Bi4Br4 strips.
Resistivity measurements in the temperature range
4–300 K along the longer axis of Bi4Br4 crystals [4],
performed on two samples, displayed a minimum at about
80 K and maximum at about 200 K. The authors of Ref. [4]
were unable to determine the absolute value of resistivity
due to difficulties in properly measuring the cross-section
of the crystals. No further literature data on the electrical
conductivity of other compounds of this type appear
to exist. The reports concerning magnetic properties
essentially only propose a diamagnetic behavior of Bi4I4
(molar magnetic susceptibility at room temperature is
ꢀ111 ꢁ 10ꢀ6 cm3/mol [5]). No computational data are
available on electronic structures of such compounds.
The present work combines results from a computa-
tional study of the electronic structures of Bi4Br4 and Bi4I4
with extensive experimental studies of the electrical and
magnetic properties of single crystals and powders of these
two compounds.
2. Experimental
2.1. Synthesis
Powdered samples of the compounds were synthesized
by annealing of stoichiometric mixtures of Bi and I in the
case of Bi4I4, and of Bi and BiBr3 (produced by the direct
reaction between bismuth metal and gaseous bromine at
250–260 1C) in the case of Bi4Br4. The duration of
annealing was 30 days at 260 1C for Bi4Br4, and 60 days
Single crystals of Bi4Br4 and Bi4I4, respectively, were
obtained from gas phase reactions according to the
methods similar to that described in Refs. [4,6]. Thor-
oughly ground mixtures of bismuth metal and HgI2 or

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at 300 1C for b-Bi4I4. The composition and purity of the
samples were confirmed by XRPD.
(FC) measurements, the samples were cooled from 310 to
5 K in a field of 200 Oe and subsequently heated in the
same field. The magnetization was measured as a function
of temperature.
2.2. Electronic structure calculations
The field dependence of the magnetization, M(H) was
also studied. The samples were subjected to a magnetic
field cycling between +10 and ꢀ10 kOe, and the magne-
tization was measured as a function of magnetic field at
temperatures of 5 and 300 K.
Quantum chemical calculations on the three-dimensional
structures of Bi4Br4 [4] and a-Bi4I4 [6] were performed
using the hybrid density functional B3LYP employing the
CRYSTAL98 program package [12]. The effective large-
core potentials (ECPs) by Hay and Wadt (HAYWLC) were
utilized for bismuth, bromine and iodine, and original
unchanged Hay and Wadt valence basis sets were used to
represent bromine and iodine valence shells [13]. The
original Hay and Wadt bismuth valence basis set was
expanded and optimized for better performance (see
Table 1). Convergence on energy was achieved in each case.
3. Results and discussion
3.1. Band structure and bonding
From the wavefunctions of Bi4Br4 and Bi4I4, as
calculated from their known three-dimensional periodic
structures, projected and total densities of states of these
two compounds were obtained, as illustrated in Figs. 2 and
3, respectively. Based on the data obtained, both com-
pounds should exhibit semiconducting behavior (the
estimated corresponding band gaps are 0.6 and 0.8 eV).
Calculated atomic charges: for Bi4Br4ꢀBi (inner) +0.17,
Bi (terminal) +0.40, Br ꢀ0.31; for Bi4I4–Bi (inner) +0.16,
Bi (terminal) +0.19, I ꢀ0.18. It is clear that due to the
higher electronegativity of bromine, as compared to iodine,
terminal bismuth atoms (i.e. those connected to halogen
atoms) bonded to bromine carry significantly higher
positive charge than the corresponding terminal bismuth
2.3. Physical measurements
2.3.1. Galvanomagnetic properties
The resistance was measured with the four-probe
method in the temperature interval 4–280 K. To single
crystals of typical size 2 ꢁ 0.05 ꢁ 0.01 mm (Bi4Br4) and
1 ꢁ 0.2 ꢁ 0.01 mm (Bi4I4) 4 contacts were soldered. Mag-
netoresistance and the Hall effect at different temperatures
were also determined. Measurements were made in the
direction of elongation of a needle-like single crystal.
Magnetoresistance and the Hall effect at different tem-
peratures in magnetic fields up to 6 T provided by a
superconducting solenoid was recorded. Measurements of
thermopower were performed at room temperature on
pressed powdered samples, synthesized by the ampoule
method described above.
2.3.2. Magnetic properties
Magnetic properties of single crystals of Bi4I4 and Bi4Br4
were investigated using a SQUID magnetometer. The
temperature dependence of magnetization, M(T) in a low
external magnetic field (H) of 200 Oe was determined. For
the zero field cooled (ZFC) measurements the samples were
cooled from room temperature down to 5 K in the absence
of magnetic field. They were subsequently heated in a
magnetic field of 200 Oe and the magnetization was
recorded as a function of temperature. For field cooled
Table 1
Optimized valence basis set for bismuth (for use with the original
HAYWLC ECP)
Shell
Exponent
s
0.6240
0.3550
0.1350
1.1550
0.3300
0.1451
0.1200
s
s
p
p
p
d
Fig. 2. Calculated projected (dashed line) and total (solid line) DOS for
Bi4Br4 structure.

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1.0
-1.0
-3.0
-5.0
-7.0
-9.0
E_Fermi
Z
X
M
Γ
Fig. 4. Band structure of Bi4Br4.
1.0
-1.0
-3.0
-5.0
-7.0
-9.0
E_Fermi
Z
Γ
X
M
Fig. 3. Calculated projected (dashed line) and total (solid line) DOS for
Bi4I4 structure.
Fig. 5. Band structure of Bi4I4.
atoms bonded to iodine atoms, while the charge differences
between inner bismuth atoms in both structures are rather
small. Figs. 2 and 3 also demonstrate that halogen p-states
in both phases are almost filled and contribute largely to
the valence bands of the respective compounds. Bismuth
atoms provide a significant contribution to the conduction
bands, with the states of inner and terminal bismuth atoms
residing almost in the same energy range. Evidently,
p-states of both types of bismuth atoms contribute to a
certain degree to the bonding to halogen atoms, while
s-states (6s lone pairs) are far below the Fermi level and do
not provide any contribution to the bonding. The only
significant difference between inner and terminal bismuth
atoms, visible in the density of states (DOS), is at the
bottom of the valence bands, with the energy lower than
about ꢀ8.2 eV. In this region of the DOS only the
contributions from terminal bismuth atoms and halogens
are significant.
Band structures near the Fermi level for Bi4Br4 and Bi4I4
are given in Figs. 4 and 5, respectively. Qualitatively
they are similar and confirm the general semiconducting
behavior of these subhalides derived from DOS calcula-
tions. It may be noted that along the X–M direction the
bands come rather close to the Fermi level as compared to
other spatial directions. This direction corresponds to the
ab plane of the unit cell, i.e. the propagation of bismuth
strips. Thus, these pictures might be taken as an indication
of anisotropic behavior; however, since at no point Fermi
level directly crosses bands in any compound, this
suggested anisotropy is of quantitative rather than
qualitative nature and does not change the semiconducting
behavior of both subhalides.
3.2. Magnetic properties
ZFC and FC temperature dependences of the magetiza-
tion [M(T)] for Bi4Br4 are shown in Fig. 6. Very similar
dependences were obtained for Bi4I4, but the absolute value
is approximately 3 times lower. Magnetization as a
function of magnetic field [M(H)] is shown in Fig. 7 for a
single crystal sample of Bi4I4, after subtracting the
diamagnetic contribution from the sample holder. Similar
data were obtained for Bi4Br4. As observed from the
figures, both materials show diamagnetic behavior. The
very small deviation from ideal diamagnetic behavior
observed at B ¼ 0 in Fig. 7 may be caused by a small
amount of some ferromagnetic impurity present in starting
materials or introduced during crystal growth from the
components. Since this ferromagnetism is very weak, it can
most probably be ascribed to the presence of magnetic
impurities with high Curie temperatures (such as iron or
nickel). EDX analyses were performed on the samples, but
no impurities could be identified down to the limit of
detection of the technique. The decrease of magnetization
seen in the ZFC M(T) data at low temperatures indicates
spin freezing.

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1107
700
600
500
400
Bi4Br4
0.014
FC MF=200 Oe
ZFC MF=200 Oe
0.012
0.010
0.008
0.006
Bi4I4
0
100
200
300
0
100
200
300
T (K)
Fig. 8. Temperature dependence of resistance.
T (K)
Fig. 6. M(T) data for a single crystal of Bi4Br4.
6
4
ductor. At the same time, the absolute values of resistivity
confirm that both compounds remain semiconductors over
the whole temperature range, so the resistivity minimum
must correspond to the transition between non-degenerate
and degenerate semiconductor behavior. We must note
here, that the resistivity minimum for Bi4Br4 was observed
by the authors of Ref. [4] and attributed to the transition
between extrinsic and intrinsic conductivity. However, our
Hall effect measurements (see below) do not agree with
such interpretation, since they show no significant change
in carrier concentration both above and below the
temperature of the resistivity minimum. (In addition, the
authors of [4] did not have the absolute resistivity values
and, therefore, could not distinguish on that basis between
a metal and degenerate semiconductor.)
300 K
2
5 K
0
-2
-4
-6
-1.0
-0.5
0.0
0.5
1.0
B (T)
We believe that such dielectrization of the energy
spectrum may be ascribed to a charge density wave
(CDW) transition. For a direct proof of the CDW at low
temperature additional experiments would be required.
The dependence of the drop in electric potential recorded
for the samples upon application of an external magnetic
field consists of even and odd parts with respect to the
magnetic field. According to convention we related the odd
part to the magnetoresistance, R(B). In both systems this
function displays positive values. The magnetoresistance of
Bi4I4 at different temperatures is shown in Fig. 9a. At low
magnetic fields B, R(B) shows a quadratic dependence on B
at all temperatures studied. At T ¼ 21 K for B42 T, R(B)
follows a linear relation with respect to the external
magnetic field. The magnetoresistance of Bi4Br4 is shown
in Fig. 9b. At T ¼ 4:2 and 23 K R(B) saturates and at
T ¼ 76 K it is very weak and displays a quadratic behavior.
Traditionally, the even part of the dependence of a drop
in electric potential upon application of an external
magnetic field to a sample is explained by the Hall effect.
The irregular geometry of the samples suggests that only a
fraction of the true Hall resistance can be calculated from
the even part of the drop in electric potential. Further, we
Fig. 7. M(H) data at 300 K and 5 K after subtracting the diamagnetic
contribution from the sample holder for a single crystal of Bi4I4.
We would also like to highlight a peculiarity in the M(T)
dependence at T ¼ (55–60 K). In this temperature range
the temperature dependence of resistance changes from
metallic-like (typical for both metals and degenerate
semiconductors) to that of a non-degenerate semiconduc-
tor (see below). At To20 K magnetization increases and
clearly shows the presence of paramagnetic impurities
discussed above.
3.3. Galvanomagnetic properties
The temperature dependences of the resistivity r for the
two samples are shown in Fig. 8. Two similar features can
be clearly seen in the temperature dependence of resistivity
for both Bi4Br4 and Bi4I4. A maximum of resistivity is
observed at T ꢂ 260 K for B4Br4 and at T ꢂ 220 K for
Bi4I4. Close to T ¼ 55 K the character of r(T) changes
from metallic-like to that of a non-degenerate semicon-

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1108
a
b
2.4
2.2
2.0
1400
4.2 K
61 K
Bi4I4
1200
Bi4Br4
1000
73 K
23 K
76 K
21 K
800
0
2
4
6
0
2
4
6
B (T)
B (T)
Fig. 9. Magnetoresistance of Bi4I4 (a) and Bi4Br4 (b).
As seen in Fig. 10, Rxy(B) follows a linear function with
respect to B. From these data it is strongly suggested that
there is only one type of charge carriers in Bi4I4. The
magnetic field dependence of Rxy(B) in Bi4Br4 is similar.
The irregular geometry of the samples, and in particular
the irregular cross-section of the samples, makes it
impossible to extract the carrier concentration from the
Hall effect. The measurements of thermopower performed
on pressed powder samples showed that the Seebeck
coefficient is negative for both Bi4Br4 and Bi4I4 (at 300 K
the values are ꢀ82 and ꢀ200 mV/K, respectively). Thus, the
charge carriers are electrons in both samples. Those
data indicate that the position of the Fermi level,
which is determined by carrier concentration (which in
turn is determined by defects of the crystal structure, in
addition to the intrinsic properties of electronic structure),
differs from that shown in Figs. 2 and 3, the band
structures of the ideal crystals at zero temperature. The
maxima of temperature dependence of resistivity observed
at high temperatures can then be explained by thermal
activation of electrons to the conduction band. The
presence of two close conduction bands may be seen
in the band structures (see Figs. 4 and 5). Thus, we
suggest that the minima of resistivity observed at
temperatures close to 50 K are caused by the formation
of a CDW in the quasi-one-dimensional degenerate
semiconductors Bi4Br4 and Bi4I4 [14]. The observed
positive magnetoresistance in Bi4Br4 (see Fig. 9b) is
typical for quasi-one-dimensional semiconductors and
metals [14,15]. In Bi4I4 (see Fig. 9a) the magnetoresistance
is different and somewhat more similar to that of
three-dimensional materials. One reason for this is the
less ionic character of bonding in this material, as
73 K
0.6
0.4
0.2
0.0
21 K
Bi4I4
0
2
4
6
B (T)
Fig. 10. Dependence of the Hall resistance on the external magnetic field
for Bi4I4 at two different temperatures.
denote this fraction as Rxy. As an example, the dependence
of Rxy on B is shown in Fig. 10 for Bi4I4 at two different
temperatures.

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1109
compared to Bi4Br4 (see below), and the more three-
dimensional character of the energy spectrum.
bismuth atoms are lower in the case of Bi4I4 (because of the
higher electronegativity of Br, as compared to I), making it
a better n-conductor, also confirmed by the experimental
resistivity measurements (see Fig. 8). Therefore, more
electrons take part in delocalization, making it possible for
neighboring bismuth strips to interact with each other.
These interactions, while no doubt too weak to be
considered bonding, could still in our view somewhat
‘‘contaminate’’ pure one dimensionality of bismuth sub-
iodide in contrast to one-dimensional subbromide.
4. Conclusions
In conclusion, we would like to emphasize several points
derived from the analysis of the combined theoretical and
experimental data. First of all, all the results from the
theoretical calculations of electronic structures of bismuth
subbromide and subiodide and the predicted respective
properties are in good agreement with the experimental
results. As is evident from both computational and
experimental data, both compounds predominantly exhibit
semiconducting behavior. Moreover, it has been shown
that electrons are the charge carriers in both cases (n-type
conductivity). This correlates very well with the fact that
bismuth metal is an n-type conductor and a poor metal (or
semi-metal) in terms of electric conductivity. Both sub-
halide structures only contain fragments of very limited
width, which essentially correspond to the two-dimensional
layers of bismuth atoms in pure metal, where a certain
degree of electron delocalization must be present. These
fragments, terminated by electronegative halogen atoms,
evidently do not have the same charge carrier concentra-
tion as bismuth metal, thus resulting in a semiconducting
behavior. The change from degenerate to non-degenerate
semiconductor at very low temperatures might involve
phase transitions; however, helium-temperature X-ray
crystallography is required in order to clarify the exact
nature of the structural changes, indicating a change in
bonding pattern, causing the alterations in the conducting
behavior.
A comparison of the behavior of the two subhalides
highlights a general similarity in their electronic structures
as well as physical properties, with one notable exception.
Of particular interest is the difference in the magnetoresis-
tance of Bi4Br4 and Bi4I4 (see Fig. 9). As mentioned above,
bismuth monobromide shows a classic one-dimensional
behavior, which is to be expected because of the
pronounced quasi-one-dimensional structural fragments
in the compound. Strangely enough, Bi4I4, which is
formally iso-structural with Bi4Br4, demonstrates serious
deviations from one dimensionality. However, this can be
rationalized using both our theoretical and experimental
data. As seen from the calculations, relative charges on
Acknowledgments
Prof. Dr. K.V. Rao and Dr. L. Belova from Stockholm
Royal Institute of Technology are gratefully acknowledged
for the magnetic measurements. This work was supported
by RFBR (grant Nos. 05-03-08186-ofi and 06-03-32789)
and Russian Presidential Grants Council (grant No. MK-
688.2006.3).
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