Introdution
In recently, Lithium-containing ternary chalcopyrite compounds with
various structural, electronic and optical properties have widely
applied in the mid- and far-infrared regions, solar cells, light
emitting diodes, nonlinear optical devices, optical frequency conversion
[1-6]. The most important characteristic is that lithium based
materials have a larger band gap and high birefringence properties,
which make them more effective in nonlinear optical materials and
femtosecond optical amplifier [7]. There are numerous theoretical
and experimental studies on Li-base ternary chalcopyrite compounds, e.g.
LiMX2 (M=Al, Ga, In and X= S, Se, Te) have received
great attention.
Previous studies have indicated that the LiMX2 (M=Al,
Ga, In and X= S, Se) belong to the orthorhombic structure, while
tellurides are described by tetragonal structure [8-9]. Our studies
on Li-Al-Te system and Li-Ga-Te system have confirmed that
LiAlTe2 [10] and LiGaTe2 [11]
are tetragonal structure at ambient condition. Many researchers have
synthesized these compounds experimentally and studied their optical
properties. Such as, Isaenko et al . [12] have synthesized the
LiMX2 crystal by using the Bridman-Stockbarger growth
technique, and measured the band-gap values and transparency ranges.
Grazhdannikov et al . [13] have obtained the
LiGaTe2 single crystal, and measured the X-ray
diffraction and optical properties. Jia et al . [14] have
grown the LiInSe2 single crystal, and systematically
studied the transmittance spectra, absorption coefficients and
refractive indices. At the same time, researchers also have carried out
many theoretical studies on the system. Ma et al . [15] have
researched the lattice dynamics and thermodynamic properties of
LiInX2 (X= S, Se, Te) by the first-principles
calculations. Lagoun et al . [16] have studied the elastic and
piezoelectric properties of LiMX2 (M= Ga, In; X = S,
Se). Chandra et al . [17] have calculated the optical
properties of LiInTe2 at different pressures using
first-principle method. The structural, electronic and optical
properties of LiInSe2 and LiInTe2 have
been researched by Ma et al with First-principle calculation
method [18]. Using the first-principles calculations method Khanet al . also have studied the anion-cation replacement effect on
the structural and optoelectronic properties of the
LiMX2 (M= Al, Ga, In; X= S, Se, Te) compounds [19].
Recent research have demonstrated that LiInSe2 has great
potential as a solar cell [20]. Subsequently, Jia et al .
[21] have found that LiInSe2 was a promising
high-performance anode material for lithium–ion batteries. In recent
years, a series of theoretical studies on LiInSe2involving the structural, electronic, optical, dynamics, thermodynamic
and optoelectronic properties [22-23]. In additional, researchers
have used experimental means to study LiInSe2 in the
growth, thermal, optical and electrochemical properties [24-25]. As
far as LiInTe2 has been concerned, the elastic,
piezoelectric, optical and electronic properties have been studied on
experimentally and theoretically [26-27].
Computational methods
In this paper, in order to find all potential stable ground state
structures of Li-In-Te system under extreme pressure, we have first
performed variable-cell structural prediction simulations using the
evolutionary algorithm [28-30] method based USPEX code. Then the
extensive structure prediction have been executed using a
swarm-intelligence based CALYPSO method and code, which enables global
structure searching in conjunction with ab initio energetic calculations
[31-32]. All structural optimizations are performed using the Vienna
ab initio simulation package (VASP) [33-34] utilizing the projector
augmented plane-wave (PAW) [35] method to describe the core-valence
interaction. The plane-wave basis-set cutoff energy is set to 600 eV,
and appropriate Monkhorst-Pack k-meshes [36] are employed with a
resolution of 2π×0.03Å-1 for Brilluin zone (BZ)
sampling. Such conditions are adopted to ensure that all the enthalpy
calculations are well converged to less than 1 meV per atom. In
geometrical optimization, all forces on the atoms converge to less than
0.05 eV Å-1. Phonon calculations are performed based on the supercell
approach [37] using the PHONOPY code [38].
Results and Discussions
In this paper, we performed variable-composition searches for stable
Li-In-Se and Li-In-Te compounds at 1 atm, 30, 50 and 100 GPa using
CALYPSO and USPEX codes. After a series of simulation calculations, the
known structures Pna 21 LiInSe2and I -42d LiInTe2 have been discovered
successfully, which are presented in the ternary diagrams named in Fig.
1. The diagrams are determined by the thermodynamic convex cell which is
a complete set of phases stable when their formation enthalpy (at T= 0
K) is negative. Meanwhile, we also uncovered several new structures at
extreme pressures,
namely,R -3m LiInSe2, ImmmLi9InSe2, P 4/mmmLi6InSe, ImmmLi9In2Se, P -3m 1
LiInTe2, ImmmLi9InTe2 and P 4/mmmLi6InTe.
In order to determine the thermodynamic stability of the Li-In-Se and
Li-In-Te system, the detailed enthalpy difference diagrams and formation
enthalpy curves as a function of pressures after the phonon calculations
are shown in Fig. 2. From Fig. 2 (a) we can learn that
LiInSe2 adopts the Pna 21 space
group at ambient condition, changes to R -3m phase at 6
GPa. LiInTe2 is stable with space groupI -42d at ambient condition, then transforms intoP -3m 1 phase at about 3.4 GPa, this process is consistent
with that of LiAlTe2 [39] and
LiGaTe2 [40] (Fig. 2 (b)). In our calculations, we
find that the formation enthalpy of Immm Li6InSe
and Li6InTe, P 4/mmmLi9InSe2,
Li9InTe2 and ImmmLi9In2Se are negative referring to
Li2Se and Li2Te (Fig. S1 (a), (b), (c)
(d) and (e)).
The new structures at different pressures we have found presented in
Fig. 3. We can learn that in R -3m LiInSe2,
the Li atoms and Se atoms form an octahedron, as well as inP -3m 1 LiInTe2, the Li atoms and Te atoms
form an octahedron.
InP 4/mmm Li6InSe, each type of atom has a
regular position, with the In atom occupying the vertex position, the Se
atom occupying the central position, and the Li atom occupying the face
and axis positions. For P 4/mmm Li6InTe,
the atoms occupy the same position as for P 4/mmmLi6InSe, but the positions look different because of the
way the primitive cells are selected. The atoms in ImmmLi9InSe2 and
Li9InTe2 occupy exactly the same
position. However, the occupation of In and Se atoms in ImmmLi9In2Se are in interchanged with those
of the two kind of atoms in ImmmLi9InSe2.
To further ascertain the dynamical stability of the new structures, we
have calculated the phonon dispersion curves of Li-In-Se system and
Li-In-Te system at 0 K using the PHONOPY code. The phonon spectrums ofR -3m LiInSe2, P -3m 1
LiInTe2, P 4/mmm Li6InSe
and Li6InTe, ImmmLi9InSe2 and
Li9InTe2, ImmmLi9In2Se, at different pressures are
chosen illustrated in Fig. 4. No imaginary phonon frequency exists in
the whole Brillouin zone indicating that all the new structures are
dynamically stable. However, several high-pressure structures become
dynamically unstable after certain pressures. Therefore, in the pressure
range we studied, the further phonon calculations combined with
thermodynamic stability, we ensure that the approximate stable pressure
ranges for R -3m LiInSe2,P 4/mmm Li6InSe, ImmmLi9InSe2, ImmmLi9In2Se, P -3m 1
LiInTe2, P 4/mmm Li6InTe,Immm Li9InTe2, are 6-30, 70-90,
40-90, 10-30, 3.4-100, 10-90 and 10-50 GPa, respectively.
The electronic properties research have been performed by the
calculations of electronic band structures of Li-In-Se system and
Li-In-Te system at different pressures. The selected electronic band
structures are displayed in Fig. 5. From Fig. 5 (a) and (c) we can learn
that Pna 21 LiInSe2 andI -42d LiInTe2 are direct band-gap
semiconductors with 1.61 eV and 1.38 eV, which are consistent with
previous studies [17-18]. We can see from Fig. 5(b),R -3m LiInSe2 is an indirect band-gap
semiconductor with 0.59 eV at 10 GPa, For other new structures (Fig. S2
(a-f)), all exhibit metallic characteristic. Interestingly, we find that
the band-gap ofPna 21LiInSe2 increase with increasing pressure. The increase
of band gap indicates the increase of optical damage threshold. This
provides a new idea for improving the nonlinear optical properties of
materials. In order to find out the reason for the increase of band gap,
the Partial Density of State (PDOS) for Pna 21LiInSe2 were calculated (Fig. 6) and it was found that
with the increase of pressure, the density of states became smooth and
the hybridization increases. Therefore, we believed that band
hybridization enhanced might be the reason for the increase of band gap.
The dielectric function is the link between the microphysical process of
transition between bands and the electronic structure of crystal, which
can reflect the band structure of solids and various kinds of light
spectral information. The dielectric function can be expressed in the
following formula:\(\varepsilon\left(\omega\right)=\ \varepsilon_{1}\left(\omega\right)+i\varepsilon_{2}(\omega)\),
where \(\varepsilon_{1}\left(\omega\right)\) is the real part,\(\varepsilon_{2}(\omega)\) is the imaginary part. The imaginary parts
of dielectric function of Pna 21LiInSe2 at 0 and 3 GPa and I -42dLiInTe2 are plotted, which is presented in Fig. 7. The
imaginary parts of dielectric function is related to the probability
that the electrons absorbing photons, which represents the energy
consumed to form the dipole. The absorption of photon by electron is the
main characteristic of electron band. From Fig.6 we can learn that the
main peak position of Pna 21LiInSe2 at 0 and 3 GPa is at 5.7 eV and 5.8 eV, the main
attribution of the peak may be from the transition of electrons from Se
p to In s orbitals. In I -42d LiInTe2, the
main peak is at 4.7 eV, the main attribution of the peak may be from the
transition of electrons from Te p to In s orbitals. The difference of
peak position indicates that the energy required for interband
transition is different. The farther the peak position is, the more
energy required for interband transition is, and the wider the band gap
of the material is. The electronic band structure shows that the band
gap of Pna 21 LiInSe2 is larger
than that of I -42d LiInTe2, which is
consistent with the location of the main peak.
Researchers have reported that the ABC2 compounds with
A-alkali metals, B-Ga, In, Tl and C-S, Se, Te are mixture of
metallic-covalent-ionic bond properties. The A-C bonds are mainly ionic,
whereas B-C bonds are preferentially covalent [40-41]. In our
calculations of Li-In-Se system and Li-In-Te system, the electronic
localization function (ELF) have been calculated, which are presented in
Fig. 8. From Fig. 8 (a) and (b) we can learn that there are localized
charge distribution between In and Se atoms for LiInSe2indicating the covalent bond properties. Meanwhile, less localized
charge distribution is seen on the Li-Se bonds, showing the ionic bond
between them. The results are similar to previous studies. However, for
LiInTe2 (Fig. 8 (c), less localized electrons
distribution between Li-Te bonds and In-Te bonds at ambient condition,
indicating a significant degree of iconicity between Li cations, In
cations and Te anions. For P -3m 1 LiInTe2(Fig. 8 (d)), the results manifest the weak covalent In-Te bonds. The
bonding properties of LiInTe2 are same as the bonding
properties for Li-Ga-Te system [42]. In addition, Figs. S3 also show
that In and Te no longer form bonds, but Li and In form ionic bonds at
high pressure in Li6InSe,
Li9InSe2,
Li9In2Se, Li6InTe and
Li9InTe2.
To further understand the bonding properties, the atoms in molecules
method (Bader charge analysis) [43] has been performed to analysis
the charge transfer. The number of electrons gained and lost in Li-In-Se
and Li-In-Te is list in Table 1. It can be found from Table 1 that for
compounds LiInSe2 and LiInTe2, the
number of electrons obtained by Se is more than that of Te, due to the
difference in electronegativity. For LiInSe2 and
LiInTe2, Li and In atoms approximately lose one electron
to form [Li]+1 and [In]+1ionic charge state, Te atoms and Se atoms gain one electron to form
[Te]-1 and [Se]+1 ionic
charge state. However, in Li6InSe,
Li9InSe2,
Li9In2Se, Li6InTe and
Li9InTe2 the In atoms gain electrons,
instead of losing electrons. Specific analysis found that all Se or Te
atoms in Li6InSe,
Li9InSe2,
Li9In2Se, Li6InTe, and
Li9InTe2 gain approximately two
electrons to form [Te]-2 ionic charge states. The
In atoms gain about three electrons in this structures to form
[In]-3 ionic charge states. In order to further
verify the valence state of In ion, the charge distributions of these
structures have been recalculated, the results are listed in Table 2. It
is shown that the valence state of In atoms is about
[In]-4 or [In]-5 ionic
charge states. The result is slightly different from that of the Bader
charge analysis, and requires a new step of verification. However, we
can confirm that In atoms in these structures will have negative valence
state when Li content increase and pressure increases.
Conclusions
In summary, the structural, electronic, optical and bonding
characteristics of Li-In-Se and Li-In-Te system have been explored below
100 GPa by first-principle theory calculations. In our calculations,
several new structures are found, namely, R -3mLiInSe2, ImmmLi9InSe2, P 4/mmmLi6InSe, ImmmLi9In2Se, P -3m 1
LiInTe2, ImmmLi9InTe2 and P 4/mmmLi6InTe. The calculations of electron band structures
for Li-In-Se and Li-In-Te system manifesting thatPna 21 LiInSe2, R -3mLiInSe2 and I -42d LiInTe2are semiconductor, other structures are metallic. Interestingly, the
band gap of Pna 21 LiInSe2increases gradually under pressure, indicating an increase in the
optical damage threshold, which provides new ideas for the subsequent
improvement of the nonlinear optical properties. The imaginary part of
dielectric function confirms the correspondence between optical spectrum
and electronic energy band. Meanwhile, we have found that the In atoms
present negative chemical valence state with Li content increasing or at
high pressure.