Pressure induced structural phase transition in SnS — An ab initio study

Abstract

The structural behaviour of SnS under pressure has been investigated by first principle density functional calculations of
the total energy by the TB-LMTO approach. We find that SnS undergoes a structural phase transition from orthorhombic type
to monoclinic type structure around 17 GPa which is in good agreement with the recent experimental study. In addition, the
ground state properties are computed and compared with the available results.

Full text

Page 1

Bull. Mater. Sci., Vol. 29, No. 1, February 2006, pp. 25–28. © Indian Academy of Sciences.
25
Pressure induced structural phase transition in SnS—An ab initio
study
M RAJAGOPALAN*, G KALPANA and V PRIYAMVADHA
Department of Physics, Anna University, Chennai 600 025, India
MS received 21 June 2005; revised 16 November 2005
Abstract. The structural behaviour of SnS under pressure has been investigated by first principle density
functional calculations of the total energy by the TB–LMTO approach. We find that SnS undergoes a struc-
tural phase transition from orthorhombic type to monoclinic type structure around 17 GPa which is in good
agreement with the recent experimental study. In addition, the ground state properties are computed and
compared with the available results.

Keywords. Electronic structure; high pressure; structural phase transition.
1. Introduction
The IV–VI compounds crystallize in several different crystal
structures. The lead chalcogenides, PbS, PbSe and PbTe and
also SnTe, adopt the NaCl structure. The compound, GeS,
has an orthorhombic crystal structure. This structure consists
of double layers of atoms, with each Ge atom coordinated
by two S atoms in the plane of the layer and one additional
S atom at a short distance perpendicular to this plane in
the same double layer. The compounds, SnS and SnSe,
form an intermediate case. These compounds have at low
temperature the orthorhombic structure but at high tempera-
ture a more symmetric structure with space group, Cmcm.
These layered semiconductors have been attracting the
attention of scientists because of their potential application
in optoelectronic devices (Shalvoy et al 1977; Trbojevic et
al 1981; Subramanian et al 2001; Nabi et al 2003). They
are also used in holographic recording systems (Parenteau
and Carlone 1990). The electronic and optical properties of
SnS and isostructural IV–VI semiconductors have been
extensively studied by electron-energy-loss spectroscopy,
photo emission spectroscopy and ellipsometry (Andersen
and Morton 1945; Lambrss et al 1974; Otto et al 1977;
Shalvoy et al 1977). Theoretical investigations by first princi-
ples calculations also have been reported (Taniguchi et al
1980; Ettema et al 1992). Experimental studies showed that
SnS is a narrow gap semiconductor with an indirect gap of
1⋅07 eV and the direct gap is located at an energy of
1⋅3 eV. But the theoretical calculation gave the value of
1⋅19–1⋅6 eV for the indirect gap and 1⋅8 eV for the direct gap.
In addition, the optical properties were also studied by optical,
infrared and Raman spectroscopy (Lambrss et al 1974;
Chandrasekar et al 1977; Yu et al 1993). The influence of
high pressure and temperature on the band gap in SnS was
studied by Parenteau and Carlone (1990) using optical
absorption spectroscopy. They have observed that under
pressure there is a reduction of both direct and indirect band
gaps. Very recently, Ehm et al (2004) investigated the struc-
tural behaviour of SnS by angular dispersive synchrotron
powder diffraction up to 38⋅5 GPa and they observed a
structural transition from orthorhombic to monoclinic struc-
ture around 18⋅15 GPa. The motivation for the present work
emerged from the above mentioned experimental work. This
is achieved by performing the electronic structure and total
energy calculation by means of the tight binding linear
muffin–tin orbital method (TB–LMTO) within the den-
sity functional formalism.
2. Computational details
Tin sulfide crystallizes in the GeS (B16) type structure in
space group, Pnma. Sn and S occupy the positions
(0⋅1194, 0⋅25, 0⋅1198) and (0⋅8508, 0⋅25, 0⋅4793), respec-
tively. The lattice parameters are taken from the experi-
mental work (Ehm et al 2004). The tight binding linear
muffin–tin orbital (TB–LMTO) method based on the lo-
cal density approximation within the framework of density
functional theory was used in the present work (Andersen
1975; Andersen and Jepsen 1984). The relativistic effect
was taken into consideration in the scalar style, but the spin
orbit coupling was neglected. The exchange correlation
potential within the local density approximation is calculated
using the parametrization scheme of von Barth and Hedin
(1972). The Brillouin zone integration was done with tetrahe-
dron method (Jepsen and Andersen 1971). The self con-
sistency is obtained in the charge density with 1728 K

*Author for correspondence (mraja1948@yahoo.co.in)

Page 2

M Rajagopalan, G Kalpana and V Priyamvadha

26
points in the entire Brillouin zone. Without breaking the
crystal symmetry, empty spheres are introduced to have close
packing. The sphere radii are chosen in such a way that the
maximum overlap between two different spheres is around
15% and charge flow is as per the electro negativity criterion.
3. Results and discussion
The electronic structure and the total energy of SnS which
crystallize in the orthorhombic structure are obtained as a
function of cell volume by performing the self consistent
band structure calculation by TB–LMTO approach in a man-
ner similar to our earlier work (Kalpana et al 1997; Raja-
gopalan and Sundareswari 2004). The total energies are
fitted to equation of state (Birch 1978) to obtain the pressure
volume relation and hence the bulk modulus. The values
are presented in table 1. From the data, we can understand
that the theoretically calculated lattice parameters differ
from the experimental value by 1⋅5% and the value of bulk
modulus is in good agreement with the reported experimental
value. In order to look for the structural phase transition,
the total energies are obtained as a function of cell volume
in the monoclinic structure also. The total energy as a function
of cell volume is presented in figure 1 for the two structure
types. One observes that the total energies of the two structure
types intersect at a critical volume indicating that SnS
undergoes a structural phase transition. The transition pressure
is obtained as the pressure at which the enthalpies of the
two phases are identical. The calculated value of the transition

Table 1. Comparison of experimental and theoretical values.
Lattice parameter (Å) Present (TB–LMTO) Experiment

a
b
c
Bulk modulus (GPa)
11⋅0123
04⋅0370
04⋅2006
39⋅55
11⋅200 (2)
3⋅987 (1)
4⋅334 (1)
36⋅6


Figure 1. Total energy vs reduced volume.
pressure is 17 GPa with a volume collapse of 6⋅3% which
is in good agreement with the recent experimental study (Ehm
et al 2004) and given in table 2. The lattice parameters at
the transition pressure are a = 11⋅55 Å, b = 3⋅741 Å, c =
7⋅373 Å and the bulk modulus is 76⋅28 GPa. The pressure
volume curve is plotted and presented in figure 2.


Figure 2. Pressure vs volume of SnS.

Figure 3. Energy band structure of SnS at ambient pressure.

Figure 4. Energy band structure of SnS in the orthorhombic
structure.

Page 3

Pressure induced structural phase transition in SnS

27
Table 2. Table indicating the volume collapse occurring in
the phase transition from the orthorhombic to the monoclinic
phase of SnS.
Present Experiment

Transition pressure (GPa)
V1 (B1)
V2 (B2)
Volume collapse (%)
17⋅0
147
158
6⋅3%
18⋅1
9⋅1%


Figure 5. b/a vs energy(ryd).



Figure 6. c/a vs energy(ryd).


The dispersion of energy bands for the selected directions
in the Brillouin zone is shown in figure 3. The overall band
profile is in agreement with those obtained by LSW
method (Ettema et al 1992). The lowest band consisting
mainly of sulfur 3s orbital are well separated from the other
bands. These bands have nearly the same energy in the large
part of the Brillouin zone. The bottom of the valence band
consists of Sn 5s states for a large part. The bands in the
middle of the valence band mostly consist of S 3p and Sn 5p
states. The maximum of the valence band is not at G but the
minimum of the conduction band is at G. There is an indirect
gap between the valence band and the conduction band of
0⋅79 eV and the direct gap is 1⋅77 eV. When the compound,
SnS, is compressed by reducing the cell volume, the band gap
starts to reduce. The decrement of the direct gap is larger than
the reduction of the indirect gap. This trend is also seen
by Parenteau and Carlone (1990) in their experimental
studies. As mentioned, the structural phase transition occurs
around 17 GPa and SnS goes to monoclinic structure
type. The band structure profile in this phase is also plotted
and given in figure 4, b/a and c/a minimizations are given
in figures 5 and 6, respectively. From the plot one observes
that SnS is again a semiconductor with an indirect gap of
1⋅64 eV. Further compression in this structure increases
the gap value.
4. Conclusions
We have studied the electronic structure of SnS in the
orthorhombic and monoclinic structure types as a function
of cell volume by first principles TB–LMTO approach. SnS is
found to be a narrow gap semiconductor with an indirect gap.
Application of pressure decreases the direct gap at a faster
rate than indirect gap. At around 17 GPa, SnS undergoes a
structural phase transition to monoclinic structure type
with a volume collapse of 6⋅3% which is in good agree-
ment with the experimental work (Ehm et al 2004). In the
monoclinic phase also SnS is in the semiconducting state
with an indirect gap of 1⋅64 eV. Further compression increa-
ses the band gap value.
Acknowledgement
One of the authors (MR) would like to thank the Max
Planck Society and Prof. O K Andersen for the hospita-
lity.
References
Andersen J S and Morton M O 1945 Proc. R. Soc. A184 83
Andersen O K 1975 Phys. Rev. B12 3060
Andersen O K and Jepsen O 1984 Phys. Rev. Lett. 53 2571
Birch F 1978 J. Geophys. Res. 83 1257
Chandrasekar H R, Humphreys R G, Zwick U and Cardona M
1977 Phys. Rev. B14 2177
Ehm L, Knorr K, Dera P, Krimmel A, Bouvier P and Mezouar
2004 J. Phys. Cond. Matter 16 3545
Ettema A R H F, de Groot R A, Haas C and Turner T S 1992
Phys. Rev. B46 7363
Jepsen O and Andersen O K 1971 Solid State Commun. 9
1763
Kalpana G, Palanivel B, Shammem Banu I B and Rajagopalan
M 1997 Phys. Rev. B56 3532
Lambrss A P, Geraleas D and Economon N A 1974 J. Phys.
Chem. Solids 35 537

Page 4

M Rajagopalan, G Kalpana and V Priyamvadha

28
Nabi Z, Kellen A, Mecabih S, Khalfi A and Benosman N 2003
Mater. Sci. Eng. B98 104
Otto A, Ley L, Azoulay J, Grandke T, Eymard R, Braun W and
Cardona M 1977 Phys. Rev. B16 4429
Parenteau M and Carlone C 1990 Phys. Rev. B41 5227
Rajagopalan M and Sundareswari M 2004 J. Alloys and Com-
pounds 379 8
Shalvoy R B, Fisher G B and Stoles P J 1977 Phys. Rev. B15
2021



Subramanian B, Sanjeeviraja C and Jayachandran M 2001
Chem. Phys. 71 40
Taniguchi M, Johnson R L, Ghijsen L and Caudano R 1980 Phys.
Rev. B42 3675
Trbojevic D, Nikelic P M, Perovic B and Cekic C 1981 Appl.
Phys. Lett. 38 362
von Barth U and Hedin L 1972 J. Phys. C5 1629
Yu L M, Degiovanni A, Thiry A, Ghijsen J and Caudano R
1993 Phys. Rev. B47 16222