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J. Phys. Chem. C 2010, 114, 16706–16709
Tunable Ionic and Electronic Conduction of Lithium Nitride via Phosphorus and Arsenic Substitution: A First-Principles Study Shunnian Wu,†,‡ Su San Neo,‡ Zhili Dong,‡ Freddy Boey,*,‡ and Ping Wu*,†,‡ Institute of High Performance Computing, 1 Fusionopolis Way No. 16-16 Connexis, Singapore 138632, and School of Materials Science and Engineering, Nanyang Technological UniVersity, Nanyang AVenue, Singapore 639798 ReceiVed: May 17, 2010; ReVised Manuscript ReceiVed: August 13, 2010
We investigated the electronic structure and transport properties of phosphorus- and arsenic-substituted Li3N using first-principles methods. It is found that both P and As partial substitution reduce Li vacancy formation energy, without appreciable alteration of energy band gap, indicating an improvement in ionic conduction. But a full substitution of P and As results in variation of crystal structure from the space group P6/mmm to P63/mmc, and the energy band gaps of Li3P and Li3As are reduced to 0.72 and 0.65 eV, respectively, in comparison with 1.14 eV of Li3N. A full substitution also brings about an increase of Li vacancy formation energies, suggesting degradation in ionic conduction. Our calculations suggest that it would be viable to achieve balanced electronic and ionic conduction of Li3N by controlled P and As partial substitution. 1. Introduction Although lithium nitride has been studied extensively both from experiments1-4 and theories,5-8 its application as a fast lithium ion conductor is inhibited by its low decomposition potential (0.44 V at room temperature). On the other hand, lithium phosphide is stable up to 2.2 V.9 Furthermore, a transition is observed from fast ionic conductor for lithium nitride to semimetallic conductor for lithium arsenide from conductivity measurements.4 However, the mechanism for the transition is undisclosed. Lithium nitride, Li3N, crystallizes in a hexagonal structure with the space group P6/mmm.3 Each N atom is surrounded by eight Li atoms in a layered configuration along the hexagonal axis consisting of one Li(2)2N layer and a layer of pure Li(1). Li3N has 1-2% vacancies in the Li2N layers, which leads to high ionic conductivity due to the hopping of lithium ions from occupied to unoccupied sites with negligible electronic conductivity.1 Disputable structures have been reported for lithium phosphide, Li3P, and lithium arsenide, Li3As. Nazri asserted that Li3P and Li3As have the same layered structure as Li3N with the alternating layers of pure hexagonal Li(1) and Li(2)2P or Li(2)2As.4,9 However, available theoretical ab initio HartreeFock calculations failed to represent the structure with experimental lattice parameters.10,11 Others claimed that Li3P and Li3As crystallize in a hexagonal structure with P63/mmc space group,12,13 which is different from Li3N. They are stacked in two alternating layers perpendicular to the c-direction. The first layer is made up of a graphite-like Li(2) and P or As layer, and the second layer is composed of a chair form cyclohexane-like Li(1) layer. However, little theoretical research has been performed to understand the underlying conduction mechanism, and few attempts have been made to rationalize the fundamental * To whom correspondence should be addressed. Tel.: 0065-64191212 (P.W.); 0065-67905609 (F.B.). Fax: 0065-64632536 (P.W.); 006567911604 (F.B.). E-mail:
[email protected] (P.W.); mycboey@ ntu.edu.sg (F.B.). † Institute of High Performance Computing. ‡ Nanyang Technological University.
electronic properties of these materials. Therefore, we investigated the electronic properties and vacancy formation of Li3N with N partially or fully substituted by P and As in this study. The structures of Li3P and Li3As were clarified. The effect of substitution on ionic and electronic conduction of Li3N was explored. 2. Methodology All energy calculations were carried out using the generalized gradient approximation (GGA) to the density functional theory (DFT), as implemented in the Vienna ab initio simulation package VASP.14 The projector-augmented wave (PAW) method with the Perdew-Burke-Ernzerhof functional was chosen to represent the ionic potential.15-17 A plane-wave basis with a kinetic energy cutoff of 400 eV was used, and reciprocal-space k-point grids were 3 × 3 × 3. Convergence with respect to k-points and energy cutoff was checked during all calculations. During geometry optimization, all atoms in the supercells were free to move according to the Hellmann-Feynman forces until the residual forces converged to be less than 0.01 eV/Å. Li3N of P6/mmm space group was structurally optimized, which gives lattice parameters of a ) 3.63 Å and c ) 3.87 Å in good agreement with the experimental values of a ) 3.64 Å and c ) 3.87 Å.3 To model a partially doped system, one N atom is replaced with P or As in a 108-atom 3 × 3 × 3 supercell, yielding a dopant concentration of 3.70 atom %. To establish clearly the effect of dopant without much interference from structural changes, the lattice parameters of doped Li3N supercells were fixed as those of Li3N supercells. Lithium vacancy was generated by removing one lithium atom close to the dopant to observe its effect more clearly. Total energy calculations were performed on Li3P and Li3As with both P6/mmm and P63/mmc space groups, respectively. Li3P and Li3As supercells of 144 atoms were built for vacancy calculations by 3 × 3 × 2 expansion of the unit cell in the selected P63/mmc structure. The atomic orbit energies of N, P, and As were calculated with inclusion of spin polarization. The atom was put in a cubic unit cell of 13 × 14 × 15 Å3, and only Γ K point in reciprocal space was used.
10.1021/jp1045047 2010 American Chemical Society Published on Web 09/13/2010
Conduction of Li3N Substituted with P and As
J. Phys. Chem. C, Vol. 114, No. 39, 2010 16707
Figure 1. Electronic band structure, density of states, and projected density of states of Li3N. The partial DOS components are as follows: s, black; px, red; py, blue; pz, green. The Fermi level is set to zero energy.
TABLE 1: Li Vacancy Formation Energy of Li3N and Li3N Doped with Dopant
Lithium vacancy formation energy EF was evaluated as
EF ) ET(V) - ET(bulk) + µLi
(1)
where ET(V) and ET(bulk) are the total energies of the supercell with Li vacancy and without vacancy, respectively; µLi is the chemical potential of the Li atom removed from the supercell to generate the vacancy. µLi can vary under a correlation of
3µLi + nµN + xµX ) µbulk
VLi(1) VLi(2)
3. Results and Discussion The electronic band structure of Li3N and density of states (DOS) and projected density of states (PDOS) of Li3N are shown in Figure 1. It shows an indirect band gap of 1.14 eV between the A and Γ points, which is consistent with previous theoretical reports.6,8,18,19 The highest valence bands are derived from N 2p states, whereas the lowest conduction bands are contributed by Li 2s states. A crystal field splitting occurs for the N 2p bands, which shifts down N pz states to lower energy. The appreciable overlapping of Li s states with N pz states indicates weak covalent bonding in the c-direction. The width of the valence band is 2.85 eV. It is noted that P or As doping does not bring about substantial change of the electronic band structure, which is not shown. Inappreciable discrepancy of the energy band gap is observed in Li3N doped with P or As. The calculated vacancy formation energies for Li3N and Li3N doped with P and As are listed in Table 1. VLi(2) is found to have much lower formation energy than VLi(1) in Li3N, which indicates that Li vacancies may predominately generate in Li(2)2N layers. This leads to an anisotropic Li ionic conduction,
Li3N/P
Li3N/As
2.22 0.51
0.38 0.20
0.03 0.08
TABLE 2: Calculated Lattice Parameters and Formation Enthalpy ∆Hf of Li3P and Li3As in Space Groups P6/mmm and P63/mmc P6/mmm
(2)
where µN and µX (X ) P, As) denote the chemical potential of N and X, respectively, and µbulk is the chemical potential of studied system. n and x are the number of constituent atoms N and X, respectively. The total energies of per atom for nitrogen gas, bulk phosphorus (P1j), and bulk arsenic (R3m j ) were chosen as the upper limits of chemical potential of nitrogen, phosphorus, and arsenic, respectively. The calculated total energies per unit formula were applied as the chemical potentials of the studied systems. We consider the Li-poor limitation in practical synthetic conditions.
Li3N
Li3P Li3As
P63/mmc
a (Å)
c (Å)
∆Hf (eV)
a (Å)
c (Å)
∆Hf (eV)
4.38 4.52
4.75 4.91
-10.8 -11.5
4.25 4.39
7.55 7.77
-14.0 -13.3
where the intralayer ionic conductivity is much greater than the interlayer ionic conductivity. Both P and As doping significantly decrease Li vacancy formation energy, and As doping displays the lowest Li vacancy formation energy. This means that Li3N doped with As would have the highest Li vacancy concentration. Since ionic conduction of Li3N relies on the hopping of Li from occupied sites to unoccupied ones, arsenic-doped Li3N would exhibit markedly improved ionic conduction. The similar formation energy values of VLi(2) and VLi(1) in phosphorous- and arsenic-doped Li3N indicate a decrease in the anisotropy of Li ionic conduction. Structural optimizations were carried out for Li3P and Li3As with the space groups P6/mmm and P63/mmc, respectively. The experimental lattice parameters of Li3P are a ) 4.23 Å, c ) 7.56 Å12 and those of Li3As are a ) 4.45 Å, c ) 7.88 Å,14 respectively. The calculated lattice parameters and formation enthalpy ∆Hf for Li3P and Li3As are listed in Table 2. It is seen that the theoretical lattice parameters of both Li3P and Li3As with the space group P6/mmm differ markedly from the experimental results, especially the c-values. Hartree-Fock calculations also give great discrepancy in the lattice parameters.11 Seel and Pandey plausibly attributed the discrepancy to polycrystalline samples used in the diffraction experiments.11 Conversely, the calculated lattice parameters of both Li3P and Li3As with the space group P63/mmc agree well with the experimental results with a maximum discrepancy less than 1.5%. Moreover, the ∆Hf values of both Li3P and Li3As with the space group P63/mmc are lower than those with the space group P6/mmm. ∆Hf is obtained by subtracting the summation of chemical potentials of constituent elements from total
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Figure 2. Electronic band structure of Li3P (a) and Li3As (b). The Fermi level is set to zero energy.
Figure 3. Density of states and projected density of states of Li3P (a) and Li3As (b). The partial DOS components are as follows: s, black; px, red; py, blue; pz, green. The Fermi level is set to zero energy.
structural energy; therefore, it can be regarded as a measure of structural thermodynamic stability.20 This indicates that the more stable structure for Li3P and Li3As is with the space group of P63/mmc. This shows that there is a structural change from P6/ mmm to P63/mmc while N in Li3N is fully substituted by P and As to form Li3P and Li3As. The calculated electronic band structures of Li3P and Li3As with the space group P63/mmc are shown in Figure 2. The valence band maximum and conduction band minimum for Li3P and Li3As are located at Γ and K points, giving an indirect gap of 0.72 and 0.65 eV, respectively. They are much lowered than the energy band gap of 1.14 eV of Li3N. However, GGA exchange and correlation functionals generally underestimate the material band gap severely.21 Though our calculations might not be able to produce the accurate band gap values, the observed trend of orderly decreased band gap from Li3N to Li3P and Li3As is unambiguous. The significantly reduced energy band gap decreases the energy required for electrons transferring from valence bands to conduction bands, which is reflected in the different colors of their prepared samples, e.g., red Li3N to brownish Li3As. This enables the rendering of electronic conduction to Li3P and Li3As via unstoichiometry or impurity. Furthermore, the valence bands of Li3P and Li3As show an increased dispersion of 3.36 and 3.41 eV in compassion of 2.85 eV of Li3N. The increased delocalization of p electrons of P
and As would increase the electron mobility. This may bring about the measured high electronic conductivity of Li3As.4 The total DOS and PDOS of Li3P and Li3As are shown in Figure 3. The valence bands are mainly contributed by 3p states of P for Li3P or 4p states of As for Li3As, and the conduction bands are mainly derived from the 2s states of Li. The increased contribution of Li s states to the dominant P or As valence bands indicates enhanced covalent character in Li3P or Li3As in comparison with Li3N. Considering that the valence bands of Li3X (X ) N, P, and As) are mainly derived from the p states of X, this indicates that the energy band gap is determined by the ionization energy of the element X. The calculated atomic orbital energies for N, P, and As in Figure 4 illustrate that the p orbital of P and As is higher in energy than that of N. Therefore, substitution for N in Li3N by P and As reduces the energy band gap. This provides a guideline to render Li3N electronically conductive and can avoid enumeration over all anions.22 The calculated Li vacancy formation energies of Li3P and Li3As are listed in Table 3. VLi(2) formation energies of Li3P and Li3As are increased in comparison with Li3N, which may be attributed to the enhanced covalent bonding between Li and P or As. The higher VLi(2) formation energy indicates that the vacancy concentration in Li3P and Li3As would be considerably lower than that in Li3N. Therefore, the ionic conductivity of
Conduction of Li3N Substituted with P and As
J. Phys. Chem. C, Vol. 114, No. 39, 2010 16709 eV, respectively. The reduction in energy band gap can facilitate the transfer of electrons from valence bands to conduction bands and, thus, gives rise to measurable electronic conduction of Li3As. The increased ionic conduction in the low doping level and the appearance of electronic conduction in Li3As suggest that it is viable to achieve balanced ionic and electronic conduction of Li3N by selecting a suitable dopant and controlling the dopant level. Since the valence bands of Li3N are mainly attributed to the p states of N, dopants with lower ionization energy would be instrumental to shrink the energy band gap. This suggests that nonmetal elements with electronegativity lower than N, such as C and Sb, would render Li3N electronic conductive for further investigation. References and Notes
Figure 4. Atomic orbital energies of N, P, and As. The red/blue arrows indicate one electron in a spin-up/spin-down state.
TABLE 3: Li Vacancy Formation Energies of Li3P and Li3As VLi(1) VLi(2)
Li3P
Li3As
0.86 0.71
0.74 0.62
Li3P and Li3As would be much lower than that of Li3N, which is consistent with the experimental observation.4 On the other hand, the formation energies of VLi(1) and VLi(2) for Li3P and Li3As are very close, which shows that there may be approximately similar vacancy concentrations in the Li(2)2P or Li(2)2As layer and Li(1) layer. This suggests an isotropic ionic conduction in Li3P and Li3As, which is different from Li3N. 4. Conclusions Lithium ionic conduction of Li3N relies on Li vacancies in the structure since it is due to the hopping of lithium between occupied sites to unoccupied sites. Phosphorous and arsenic doping can effectively reduce Li vacancy formation energy, which would significantly increases Li vacancy concentration. However, full substitution for N by P and As brings about a change of crystal structure from space group P6/mmm for Li3N to P63/mmc for Li3P and Li3As. Li vacancy formation energy in Li3P and Li3As is remarkably increased, which leads to depression of ionic conduction. Full substitution by P and As also remarkably reduces the energy band gap by 0.42 and 0.49
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