Solid State Communications Structural stability and electronic

Solid State Communications 150 (2010) 669–674
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Solid State Communications
journal homepage: www.elsevier.com/locate/ssc
Structural stability and electronic properties of LiNiN
C.H. Hu a , Y. Yang b , Z.Z. Zhu a,∗
a
Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, China
b
State Key Lab for Physical Chemistry of Solid Surfaces, Xiamen University, Xiamen 361005, China
article
info
Article history:
Received 10 February 2009
Received in revised form
6 December 2009
Accepted 11 December 2009
by E.G. Wang
Available online 21 December 2009
Keywords:
A. LiNiN
D. Structural stability
D. Electronic structures
E. First-principles calculations
abstract
The structural stability and electronic properties of layered nitridometallate LiNiN have been investigated
by first-principles calculations based on the density functional theory. Experiments show that LiNiN
has a hexagonal structure, with alternate LiN and Ni planes stacking perpendicular to the Ni–N chains.
However, our calculation shows that LiNiN in the simple tetragonal structure (D94h ) is more stable than the
hexagonal one (D3h ). The phase transition between the hexagonal and tetragonal structures was discussed
by supposing a medial phase and by calculating the transition pressure and energy barriers between them.
The results suggest that the pressure-induced phase transition from tetragonal LiNiN to hexagonal one
should be triggered by a negative pressure. Furthermore, electronic structure calculations suggest that
tetragonal LiNiN may be more conductive than that of hexagonal phase, and the electronic conductivity
of tetragonal LiNiN is isotropic, other than the anisotropic one for hexagonal LiNiN.
© 2009 Elsevier Ltd. All rights reserved.
In recent decades, lithium late transition-metal nitrides have
attracted significant interest owing to their special crystal
structures, complemented by their promising electrochemical
performance and potential applications as anode materials in
lithium ion batteries. Although a great deal of effort has been
devoted to the study of the performance of lithium ion batteries,
even greater scientific efforts are still required to search for new
materials that can replace the current ones. The potential of lithium
nitridometallates being used as the anode material in rechargeable
lithium batteries has been demonstrated, and a very high specific
capacity ranging from 700 to 800 mAh/g was exhibited [1,2].
Moreover, from the angle of security, the stability of the electrode
materials in lithium ion batteries is of special importance, which
gives rise to the demand for alternative and safer materials.
Recently, considerable attention has been paid to the novel layered ternary nitride LiNiN mainly for the interesting combination
of fast Li+ ion diffusion and its exhibition of special metallic behavior which enables it to be applied as the electrode material
for lithium ion batteries [3]. Stoeva et al. [3,4] studied in detail
the crystal and electronic properties of hexagonal LiNiN (denoted
by hex-LiNiN also as phase A) both experimentally and theoretically. They reported that the layered nitridometallate hex-LiNiN
contains a large number of inherent Li+ ion vacancies and shows
distinctive and anisotropic electronic conductivity, which may be
induced by the infinite Ni–N chains in its crystal structure [5].
Structurally, there are many other kinds of compounds reported,
∗
Corresponding author. Tel.: +86 592 2182248; fax: +86 592 2189426.
E-mail address: [email protected] (Z.Z. Zhu).
0038-1098/$ – see front matter © 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ssc.2009.12.020
possessing one-dimensional (1-D) Ni–N chains (such as CaNiN [6]
and Li3 Sr3 Ni4 N4 [7] as the representatives), while the arrangements of the chains vary with one another. Each of these ternary
nitrides is interesting in its structural chemistry which is uncommonly seen in transition-metal complexes. The 1-D Ni–N chains in
these ternary nitrides lead to low coordination numbers and lowspin states for Ni as well as the interesting electronic and magnetic
properties [3].
The hexagonal structure LiNiN, with alternate LiN and Ni planes
stacking perpendicular to the Ni–N chains, has been synthesized
in experiments. And, much work has been done concerning
hexagonal LiNiN [3,4,8] and also CaNiN [9–12]. However, LiNiN in
other structures, such as in the tetragonal structure of CaNiN, has
not been synthesized in the experiment. Therefore, less attention
has been paid to the structural stability of LiNiN. In this paper,
we present the structural stabilities and electronic structures
of LiNiN systems, including equilibrium structural parameters,
binding energies, phase transition pressure, energy barriers and
electronic properties.
The calculations were performed with Vienna ab initio simulation package (VASP) which is based on the density functional theory, plane-wave basis and projector augmented wave
(PAW) representation [13–15]. The exchange–correlation potentials were approximated by both the localized density approximation (LDA) [16] and generalized gradient approximation (GGA)
given by Perdew and Wang [17,18]. The wave functions were expanded in a plane-wave basis set with the kinetic energy cutoff up
to 33.07 Ry and 40.42 Ry for the hexagonal and tetragonal LiNiN,
respectively. The integration over Brillouin zone (BZ) was replaced
by the discrete summation over a special set of k-points based on
670
C.H. Hu et al. / Solid State Communications 150 (2010) 669–674
a
b
Fig. 1. Crystal structures of (a) hexagonal LiNiN and (b) tetragonal CaNiN.
a
b
Fig. 2. Binding energy as a function of unit-cell volume for (a) LiNiN and (b) CaNiN.
the Monkhorst–Pack scheme [19]. Meshes of 13 × 13 × 15 and
15 × 15 × 11 Monkhorst–Pack k-points corresponding to 168
and 216 special points in the irreducible Brillouin zone were employed for hexagonal and tetragonal structures, respectively. Both
kinetic energy cutoff and Monkhorst–Pack k-point mesh were optimized so that the total energy change was less than 1 meV
when the cutoff and k-point mesh were increased. Although spinpolarization is distinct in the electronic structure of Ni, we do not
attempt to include this effect because our calculations showed
that all the hexagonal and tetragonal LiNiN’s are insensitive to the
spin-polarized effect. The differences between the spin-polarized
calculation results and non-spin-polarized ones are ignorable.
Gaussian smearing method was introduced to determine the partial occupancies fnk in the present calculation. Optimization of
the crystal structures was achieved with conjugate-gradient technique, and the calculated Hellmann–Feynman forces were used as
a guide [20]. All crystal geometries were fully relaxed until the
forces upon all atoms were less than 5 meV/Å. Therefore, the obtained structures were all in stable or meta-stable phase.
In the crystal structure of hex-LiNiN, alternate LiN and Ni planes
stack perpendicular to the Ni–N chains [5,21]. The LiN planes were
linked via infinite and linear Ni–N chains, as shown in Fig. 1(a). In
contrast, in the crystal structure of CaNiN (in tetragonal lattice),
Ca occupied 2e positions: (0,0,1/4) and (0,0,3/4); Ni occupied
2b positions: (1/2,1/2,0) and (1/2,1/2,1/2); and N occupied 2c
positions: (0,1/2,0) and (1/2,0,1/2). All the 1-D Ni–N chains in hexLiNiN were parallel to each other, while the non-intersecting linear
Ni–N chains crisscrossed the structure of CaNiN [6]. Firstly, we
present our calculation results of CaNiN in tetragonal structure in
order to verify our calculations. The computation for CaNiN was
performed under a cutoff energy of 36.75 Ry and with a 15 × 15 × 8
Monkhorst–Pack k-points mesh corresponding to 180 special kpoints. The calculation results show that the lattice constants of
the CaNiN in tetragonal structure are a = 3.57 Å and c = 7.09 Å,
which is in excellent agreement with other theoretical values of
a = 3.57 Å and c = 7.08 Å [12] as well as the experimental values
of a = 3.58 Å and c = 7.01 Å [6].
In the present work, both the hexagonal (Fig. 1(a)) and
tetragonal (Fig. 1(b)) structures for LiNiN and CaNiN are studied.
LiNiN in the tetragonal structure is denoted by tetra-LiNiN and
also as phase C. The binding energy (defined as the difference
between the total energy of the system and sum of the atomic
energies) as a function of the unit-cell volume for the two
systems are shown in Fig. 2(a) and (b). Fig. 2 show that both
LiNiN and CaNiN in tetragonal structure can be more stable than
those in hexagonal structure. The binding energy of tetra-LiNiN
is −12.22 eV/unit-cell, which is lower than −11.96 eV/unitcell of hex-LiNiN. The binding energy of tetragonal CaNiN is
−14.15 eV/unit-cell, which is also lower than −13.70 eV/unitcell for CaNiN in hexagonal structure. The result for CaNiN is
consistent with the experimental data [6], showing that CaNiN is
in a tetragonal structure. However, experiments [3,4,8] show that
the structure of LiNiN was hexagonal rather than tetragonal. Why
was the LiNiN in tetragonal structure not seen in experiments?
To answer this question, we will calculate the pressure required
for the phase transition as well as the energy barrier between the
hexagonal and the tetragonal structures of LiNiN.
In order to study the phase transition between hex-LiNiN and
tetra-LiNiN, a medial phase (denoted by med-LiNiN also as phase
B) was introduced, as shown in Fig. 3(b). Correspondingly, ab
initio calculations were performed on the potential energy barriers
between phase A and phase B, and then, from the phase B to
phase C. The supercells of ternary nitrides (hex-LiNiN, med-LiNiN
and tetra-LiNiN) are illustrated in Fig. 3(a)–(c), respectively. The
corresponding binding energy of the med-LiNiN is −12.14 eV/unitcell, which is slightly higher than −12.22 eV/unit-cell for tetraLiNiN and slightly lower than −11.96 eV/unit-cell for hex-LiNiN.
3
Moreover, the cell volume gradually shrank from 39.105 Å for
3
hex-LiNiN to 32.468 Å for tetra-LiNiN. The calculation results of
hex-LiNiN, med-LiNiN and tetra-LiNiN are listed in Table 1.
Fig. 4(a) shows the potential energy barrier between phase A
and phase B (denoted by EAB ), and then, from phase B to phase C
(denoted by EBC ). The potential energy barriers EAB and EBC , which
C.H. Hu et al. / Solid State Communications 150 (2010) 669–674
a
b
671
c
Fig. 3. Primitive cell for (a) hex-LiNiN, (b) med-LiNiN, and (c) tetra-LiNiN.
Table 1
Lattice constants, nearest neighbor bond lengths of Ni–N and Li–N, unit-cell volumes, and binding energies of hex-LiNiN, med-LiNiN and tetra-LiNiN.
hex-LiNiN
med-LiNiN
tetra-LiNiN
a
This work
Experimenta
This work
This work
a (Å)
c (Å)
Ni–N (Å)
Li–N (Å)
V (Å3 )
E (eV)
3.632
3.739
3.089
3.448
3.423
3.523
3.445
5.462
1.712
1.762
1.722
1.742
2.097
2.158
2.181
2.193
39.105
42.654
32.872
32.468
−11.96
–
−12.14
−12.22
Ref. [3].
a
b
Fig. 4. (a) Potential energy barriers from phase A to phase B and from phase B to phase C. All energies are shown in eV. (b) Binding energy of hex-LiNiN and tetra-LiNiN as a
function of unit-cell volume. The energy of tetra-LiNiN at equilibrium has been chosen as the zero-energy, the reference point. The volume was normalized to the equilibrium
volume of tetra-LiNiN. The dotted lines represent the common tangent to the equations of state for hex-LiNiN and tetra-LiNiN.
were calculated with the nudged elastic band (NEB) method [22],
are estimated to be 0.44 and 0.90 eV/cell. The NEB method works by
optimizing a number of intermediate images between two phases,
where the shape and size of all intermediate images are fixed to be
the same to each other while for each image the atomic positions
are allowed to be relaxed. The calculated energy barriers using
the NEB method might be overestimated since the lattices of the
intermediate states are fixed during the calculations. The EBC is
shown to be remarkable, if EAB is not so large. Experimentally, hexLiNiN, maintaining the parent hexagonal structure of Li3 N, was
synthesized by reaction of Li3 N powder with nickel foil which was
sealed in a reaction vessel under nitrogen at ambient pressure and
heated at 730–750 ◦ C for 7 days [3]. The experimental temperature
seemed to be relatively low and should not reach the value for the
required phase transition between hex-LiNiN and tetra-LiNiN.
Both the external temperature and pressure play important
role in phase transitions. Consequently, we studied the external
pressure of the phase transition from tetra-LiNiN to hex-LiNiN. It is
well known that the phase transition induced by external pressure
occurs along the common tangent line between the E (V ) curves of
the two phases, and the transition pressure Pt can be expressed as
the negative slope of common tangent line. The initial and the final
transition energies and transition volumes are determined by the
tangent points [23]. Normalized to the equilibrium volume of tetraLiNiN and using energy of tetra-LiNiN at equilibrium as the zeroenergy point, the energy curves of hex-LiNiN and tetra-LiNiN as a
function of volume are shown in Fig. 4(b). The calculated transition
volumes (VtA and VtC ), the relative energy difference 1Et and the
transition pressure Pt are listed in Table 2. The calculations suggest
that the phase transition from tetra-LiNiN to hex-LiNiN should be
triggered by negative pressure which is estimated to be −5.71 GPa
and −7.69 GPa from GGA and LDA, respectively, as shown in
Table 2. Therefore, a tremendous negative hydrostatic pressure
should be applied in order to induce a phase transition from hexLiNiN to tetra-LiNiN. So far, phase transition induced by negative
pressure has been investigated mainly theoretically [24,25], for
example, phase transition within the tetragonal space group
P4 mm associated with anomalous enhancement of tetragonality
in PbTiO3 and BaTiO3 under negative hydrostatic pressure was
theoretically predicted by Tinte et al. [25], who also developed
a phenomenological model to describe the phase transition. In
short, hexagonal rather than tetragonal LiNiN was observed in
experiment could be due to the high energy barrier and the
large negative transition pressure required for the structural
transition.
In order to grasp the nature of interaction in the LiNiN systems,
we plot in Fig. 5 the electron charge density differences on the
plane crossing the Ni–N chains and the Li–N plane for hex-LiNiN,
med-LiNiN and tetra-LiNiN, respectively. The electron charge
density difference is defined as the charge density difference
between LiNiN and the superposition of atomic charge densities,
P
Eµ ), where ρatom (Er − REµ )
i.e., 1ρ(E
r ) = ρ(E
r) −
r − R
µ ρatom (E
672
C.H. Hu et al. / Solid State Communications 150 (2010) 669–674
a
b
Fig. 5. Contour plots of charge density differences for (a) Ni–N chains and (b) Li–N planes of hex-LiNiN, med-LiNiN and tetra-LiNiN, respectively. Solid and dashed lines
correspond to 1ρ > 0 and 1ρ < 0, respectively. The interval values are chosen as 0.06 and 0.015 e/Å3 for (a) and (b), respectively.
Table 2
A ,C
The calculated transition volumes (Vt ), total energy difference (1Et ) and
transition pressure (Pt ) for hex-LiNiN and tetra-LiNiN. Volumes are normalized to
the equilibrium volume of tetra-LiNiN.
GGA
LDA
1Et (eV)
VtC
VtA
Pt (GPa)
0.233
0.439
1.07
1.08
1.27
1.36
−5.71
−7.69
is the atomic charge density. Such a plot can help to visualize
the characteristic of bonding. In Fig. 5, the charge accumulation
(solid lines) and depletion (dashed lines) regions relative to
the non-interacting atoms are clearly shown. From Fig. 5(a),
strong covalent, i.e., significantly directional charge accumulation
between the atoms, and some ionic characters for the bonding
(interactions) between the N and Ni atoms are clearly visible
for all the hex-, med- and tetra-LiNiN. The ionic bonding was
judged by the maximum values of charge depletion and charge
accumulation contour lines as well as the density of the lines (the
scale of the lines has been drawn in the plots). Fig. 5(a) shows
that the charge depletion around Ni is larger than the charge
accumulation between N and Ni atoms, suggesting electrons loss
around Ni atoms. In the same way, an ionic (largely) mixed with
covalent interaction between Li and N atoms in the hex-LiNiN,
med-LiNiN and tetra-LiNiN can be seen in Fig. 5(b), discussions
on the mixed ionic and covalent bonding characters can also be
found in Refs. [26,27]. However, the ionic interaction is found
to be gradually strengthened from hex-LiNiN to med-LiNiN and
then to tetra-LiNiN. The reason for significantly differences in the
bonding picture in Fig. 5(b) is due to their different structures and
different atomic surroundings. Both the charge redistribution plots
illustrate that the interactions in hex-LiNiN, med-LiNiN and tetraLiNiN are strong, and the strong covalent bonding in the Ni–N
chains accounts for the structural stability of LiNiN. The structural
stability implies that hex-LiNiN tends to remain its hexagonal
structure in experiment if there is no strong external influence.
The lower energy of tetragonal LiNiN relative to hexagonal LiNiN
may be due to the larger coordination number of N atoms in the
tetragonal LiNiN, which leads to the change of the abundance of
bonding formed in LiNiN.
The calculated band structures of LiNiN systems are shown
in Fig. 6 where the Fermi level is set at 0 eV. In the band
structure of hexagonal LiNiN shown in Fig. 6(a), the bands cutting
the Fermi energy are all in the directions parallel to the c-axis
(i.e. directions of Ni–N chains), i.e., along the 0 –A, K–H and M–L
lines in the BZ. As expected, the energy bands of a hexagonal
structure which suggests no significant inter-chain interactions are
rather flat, except in the directions parallel to the c-axis where they
crossed the Fermi level. The band structure of hex-LiNiN, therefore,
indicates an anisotropic electronic conductivity, as already shown
by a combination study of experiment and theory [3]. For the medLiNiN, there are bands along the 0 –Z and A–M (Fig. 6(b)), which
are parallel to the directions of Ni–N chains, crossing the Fermi
level, besides, there is also a flat band along direction R–A, which
is not parallel to the directions of Ni–N chains, crossing the Fermi
level. This indicates that the conductivity of med-LiNiN is no longer
fully anisotropic. Furthermore, the band structure of tetra-LiNiN,
as shown in Fig. 6(c), indicates that the electronic conductivity of
tetra-LiNiN is isotropic. That is, bands crossing the Fermi level are
in all the directions instead of only in the directions parallel to the
c-axis in hexagonal LiNiN.
The total electronic density of states (TDOS) and the partial
density of states (PDOS) of LiNiN systems are presented in
Fig. 7. It can be seen that, for hex-LiNiN and med-LiNiN, the
electronic states at the Fermi level are mostly contributed by
N–(px , py ) and Ni–(dxz , dyz and d2z ) and a small part by N–pz and
Ni–(s, dxy and dx2 −y2 ) states. While for tetra-LiNiN, electronic states
at the Fermi level are mostly from N–pz and Ni–(dxz , dyz and d2z )
states and a small part from N–(px , py ) and Ni–(s, dxy and dx2 −y2 )
states. The calculated TDOS at the Fermi level are about 1.50,
1.51 and 1.65 states/(eV.cell) for hex-, med- and tetra-LiNiN,
respectively. Since the density of states at the Fermi level is
one of the main factors determining the electrical conductivity
of a material, this might suggest that tetra-LiNiN could own the
highest electronic conductivity. In more detail, within the energy
range from about −7.0 eV to the Fermi level for hex-LiNiN and
med-LiNiN, there are approximately three regions distinguished
by their bonding characteristics [3]. Fig. 7(a) and (b) show that
Ni d2z –N pz σ -bonds are in the region from −7.0 eV to around
−5.5 eV, and Ni(dxz , dyz )–N(px , py )π -bonds between −5.5 eV and
−4.0 eV. Moreover, the non-bonding states Ni (dxy , dx2 −y2 ) locates
in the region approximately from −3.0 eV to the Fermi level and
from −4.0 eV to the Fermi level. So, for hex-LiNiN and med-LiNiN,
the interactions between Ni and N atoms are mixed with π - and
C.H. Hu et al. / Solid State Communications 150 (2010) 669–674
a
b
673
c
Fig. 6. Band structures of (a) hex-LiNiN, (b) med-LiNiN, and (c) tetra-LiNiN. The first Brillouin zone for hex-, med-, and tetra-LiNiN are presented at the lower-left corner of
each figure, respectively.
a
b
c
Fig. 7. TDOS and PDOS for (a) hex-LiNiN, (b) med-LiNiN, and (c) tetra-LiNiN. s-PDOS represented by black, px , py by red, pz by blue, dxz , dyz by olive, dxy , dx2 −y2 by magenta
and dz2 by cyan, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
σ -bonding characters. Comparatively, the TDOS and PDOS plots in
Fig. 7(c) show that for tetra-LiNiN the N pz –Ni (dxz , dyz )π -bonding
Acknowledgements
interactions occur approximately in the energy region between
−7.0 eV and −3.0 eV, despite the absence of Ni d2z –N pz σ -bonds.
In the region of −7.0 eV to the Fermi level, it is still occupied by
the non-bonding states of Ni(dxy , dx2 −y2 ) orbits. In other words, for
tetra-LiNiN the interactions between Ni and N atoms are with only
π -bonding character.
In summary, first-principles density functional calculations
were employed to study the structural stability and electronic
properties of LiNiN. It was found that LiNiN in tetragonal
structure is more stable than the one in hexagonal structure,
while experiments show that the structure of LiNiN is hexagonal
rather than tetragonal. The phase transition pressure of LiNiN
from tetragonal to hexagonal structure as well as the potential
energy barrier between the phases had been presented. The
phase transition was found to be triggered by a negative pressure
estimated to be around −5.71 GPa and −7.69 GPa, respectively,
calculated with GGA and LDA. Moreover, qualitative studies show
that energy barriers are remarkable. These results should account
for the experiment in which only the hexagonal structure of LiNiN
was observed. Calculations of electronic structures suggest that
the strong covalent interactions in the Ni–N chains account for
the structural stability of LiNiN systems. Furthermore, unlike hexLiNiN which has anisotropic electronic conductivity, conductivity
of tetra-LiNiN is isotropic.
Financial support is provided by the National Natural Science
Foundation of China (Grant No.10774124) and the National 973
Program of China (No. 2007CB209702).
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