Role of Lithium Ordering in the LixTiO2 Anatase → Titanate Phase

LETTER pubs.acs.org/JPCL

Role of Lithium Ordering in the LixTiO2 Anatase f Titanate Phase Transition Benjamin J. Morgan* Department of Materials, University of Oxford, Parks Road, OX1 3PH, United Kingdom

Graeme W. Watson* School of Chemistry and CRANN, Trinity College Dublin, Dublin 2, Ireland

bS Supporting Information ABSTRACT: The mechanism of the tetragonal T orthorhombic phase separation of Li-intercalated anatase TiO2 has previously been proposed to be a cooperative Jahn
Teller distortion due to occupation of low-lying Ti 3dxz,yz orbitals. Using density functional calculations, we show that the orthorhombic distortion of Li0.5TiO2 is not a purely electronic phenomenon and that intercalated Li plays a critical role. For a 2  1  1 expanded supercell for 0 e x(Li) e 1, the intercalation voltage is minimized for x(Li) = 0.5. The low-energy structures display a common structural motif of edge-sharing pairs of LiO6 octahedra, which allows all Li to adopt favorable oxygen coordination. Long-ranged disorder of these subunits explains the apparent random Li distribution seen in experimental diffraction data. SECTION: Statistical Mechanics, Thermodynamics, Medium Effects

T

he intercalation of lithium into suitable electrodes is one of the fundamental processes underlying Li-battery technologies. One potential anode material is anatase TiO2,1
4 but its use is complicated by a transition from the tetragonal anatase phase at low lithium concentrations to an orthorhombic titanate phase with approximate composition Li0.5TiO2.5,6 This occurs as a phase separation where Li-rich domains undergo reversible growth as lithium is progressively intercalated under an applied voltage. This phase separation is thought to govern much of the electrochemistry of anatase electrodes, with lithium diffusion and therefore charge/discharge rates and maximum output power determined by transport between domains.7 In bulk samples, the maximum lithium concentration achievable under electrochemical intercalation is x(Li) ≈ 0.5, corresponding to the entire sample having transformed to the orthorhombic phase. Stoichiometries up to LiTiO2 have been reported in nanocrystals as the small particle size prevents the coexistence of tetragonal and orthorhombic domains.8
10 Intercalation of Li into TiO2 can be described as xLi(s) + TiO2 T LixTiO2 + e
, with accommodated lithium present as Li+, and compensating electrons transferred to Ti 3d orbitals, which are formally unoccupied in stoichiometric TiO2. It has been proposed that the anataseftitanate phase transition is a cooperative Jahn
Teller (CJT) distortion that occurs as Ti 3d orbitals are progressively occupied.11,12 In anatase TiO2, the titanium atoms have D2d symmetry, with crystal field effects placing the 3dxy orbitals below the degenerate 3dxz,yz pair. The CJT mechanism of r 2011 American Chemical Society

Koudriachova et al. is as follows: At low lithium concentrations, the Ti 3dxy orbitals are occupied by the donated excess charge due to the intercalated lithium. At higher lithium concentrations, the highly localized nature of the 3d orbitals makes it unfavorable to add further charge to these 3dxy orbitals and the 3dxz,yz orbitals are filled instead. By orthorhombically distorting with a 6¼ b the degeneracy of the 3dxz,yz pair is lifted. This electronic model, however, makes no predictions about the donated electron density (and corresponding Li concentration) necessary for such a Jahn
Teller distortion nor does it explain why phase separation occurs rather than a simple transition within a single domain. Here we report a density functional theory study of the intercalation of Li into anatase TiO2 across the range 0 e x(Li) e 1. We find that: (a) Adding electrons to the Ti 3d states is not sufficient to stabilize an orthorhombic distortion, showing that the CJT model fails to explain this phase separation behavior. The presence of lithium is necessary, suggesting the interaction between intercalated Li and the host lattice is critical. (b) Considering all symmetry inequivalent lithium configurations within an extended supercell, the intercalation energy per lithium is a minimum for x(Li) = 0.5. (c) For x(Li) < 0.5 the system energy is minimized by phase separation into regions of low lithiumdensity anatase and the orthorhombic Li0.5TiO2 phase. (d) For Received: May 27, 2011 Accepted: June 17, 2011 Published: June 17, 2011 1657

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Figure 2. Distribution of excess charge with GGA and GGA+U for a 1  1  1 cell with two intercalated lithium ions [+2 Li] or two electrons [+2 e]. The charge isosurfaces are drawn at 0.05 eÅ
3. Figure 1. Two lithium configurations for Li0.5TiO2 within a 1  1  1 unit cell. Red atoms are oxygen, blue are titanium, and purple are lithium.

Table 1. Optimized Lattice Parameters for 1  1  1 TiO2 Cells That Are Either Stoichiometric or Have Two Additional Electrons or Lithium Atoms, Calculated Using GGA and GGA+U a

b

c

a/b

GGA

3.823

3.822

9.716

1.00

GGA [+2e
]

4.011

4.011

9.940

1.00

GGA [+2Li]A

4.048

3.932

9.119

1.03

GGA [+2Li]B

4.068

3.927

9.069

1.03

GGA+U

3.908

3.908

9.696

1.00

GGA+U [+2e
] GGA+U [+2Li]A

4.150 4.149

4.150 4.010

10.120 9.534

1.00 1.03

GGA+U [+2Li]B

4.162

3.968

9.499

1.05

x(Li) > 0.5, we predict a similar phase separation between Li0.5TiO2 and LiTiO2, in agreement with experiment.13 The three lowest energy Li configurations at x(Li) = 0.5 are constructed from differently arranged pairs of edge-sharing LiO6 octahedra, which allows shortened Li
O distances along Æ100æ, enhancing the Coulomb stabilization of the Li. We propose that these Li2O12 units characterize the orthorhombic titanate phase, where variation in relative orientation explains the absence of supercell reflections in experimental X-ray diffraction data.14 As the simplest model for Li0.5TiO2, we consider a 1  1  1 anatase cell with two interstitial lithium atoms. This allows two inequivalent lithium arrangements, labeled A and B in Figure 1. Both GGA and GGA+U predict that stoichiometric Ti4O8 is tetragonal (a = b), whereas A and B are orthorhombic with a 6¼ b (Table 1). The distribution of excess charge donated from the intercalated Li differs for the two calculation methods. With GGA, this charge is delocalized over all atoms (Figure 2), corresponding to partial occupation of the bottom of the conduction band to give a metallic state. This contradicts experimental conductivity measurements15 and valence photoelectron spectroscopy (XPS), which shows that occupied states produced upon Li intercalation are well-separated from the bottom of the conduction band.16 This discrepancy is due to the inherent selfinteraction error from which standard density functionals suffer. Using GGA+U, the excess electrons are localized at two Ti centers in 3d orbitals, with the corresponding occupied states now split from the conduction band minimum, recovering agreement with the experimental XPS.16 The CJT mechanism proposes that the stability of orthorhombic versus tetragonal structures simply depends on the number of electrons donated

Figure 3. Intercalation voltages in electronvolts. The blue circles are values for all symmetry inequivalent configurations within a 2  1  1 supercell. The red triangle corresponds to a single Li in a 4  4  1 supercell and approximates the dilute limit. The dashed line is the ground-state energy versus composition curve.

to the Ti 3d orbitals. Geometry optimizations of stoichiometric anatase TiO2 with two additional electrons and a compensating uniform background charge, to give Ti4O8:e
2 , give an orthorhombic cell, even when the initial geometry is constructed with an orthorhombic distortion of a/b = 1.04 (Figure 2 and Table 1). Therefore, the orthorhombic lattice distortion observed for Li0.5TiO2 is not explained by simply donating electrons to the Ti 3dxy,xz states. Instead, the presence of the intercalated lithium is necessary to stabilize the orthorhombic titanate phase. To examine further the Li
lattice interaction, we performed a series of GGA+U geometry optimizations for LixTi8O16 (a 2  1  1 supercell). For each x(Li), all symmetry inequivalent arrangements of Li were generated with the SOD code of Grau-Crespo et al.17 The configurations with the lowest energy per Li are found for x(Li) = 0.5 (Figure 3). The set of lines that connects the lowest energy ordered phases produces the ground-state energy versus composition curve.18 Any structures with energies above this line are unstable with respect to a mixture of the two structures that define the neighboring end points. For x(Li) < 0.5, the system energy will be minimized by phase separation into Li0.5TiO2 and the low x(Li) anatase phase. Similarly, for x(Li) > 0.5, the system will phase-separate into regions with composition Li0.5TiO2 and LiTiO2, as seen in nanocrystalline samples.13 Koudriachova et al. reported a 0.001 eV per formula unit energy difference between the A and B 1  1  1 Li0.5TiO2 configurations described above and proposed that Li is randomly distributed throughout the interstitial sites in the titanate phase.12 The large variation in intercalation voltages in Figure 3 shows that this is not the case. Figure 4 shows a schematic of the 10 Li configurations for the 2  1  1 supercell, at x(Li) = 0.5, 1658

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Figure 4. Ten nonequivalent Li configurations for x(Li) = 0.5 within a 2  1  1 supercell in order of increasing energy. Energies relative to the ground state are given in meV Li
1.

Figure 6. Upper panel: LiO6 octahedra in the three low-energy configurations (i)
(iii) for x(Li) = 0.5. Lower panel: Schematic diagrams of the relative ordering of the Li2O10 octahedral pairs in each structure. All three structures can be constructed from identical (010) planes that differ only in their relative orientation.

Figure 5. (a) Schematic of the ground-state configuration (i) showing the alternating distortion of the octahedral interstitial sites. (b) Coordination geometry for the paired Li-occupied octahedra.

ordered by their relative energy. The configurations that are formally equivalent to the 1  1  1 arrangements A and B (Figure 4(viii)
(x)) are highest in energy.19 The highest energy configurations for x(Li) = (0.25,0.75) also correspond to the Li configurations that would be generated using a single Li in a 1  1  1 cell. Calculations performed on single unit cells thus poorly represent the energetics of the system due to the constrained high symmetry, and this needs to be considered when modeling Li intercalation in other host materials. All three lowest energy configurations, with x(Li) = 0.5, display common features in their Li arrangement. Within the 2  1  1 supercell, only a single Li is found in each xy plane, and this requires that pairs of Li occupy adjacent xz-edge-sharing octahedra. yz-edge sharing between LiO6 octahedra produces small increases in the intercalation energy, but not to the extent that these configurations are destabilized with respect to those where there are pairs of corner-sharing octahedra in the xy plane (Figure 4(iv)
(x)). For configuration (i), along the expanded direction the O
O distance for Li-occupied interstitial sites is 3.87 Å, compared with 4.42 Å for vacant interstitial sites and 3.91 Å for all sites in the dilute-Li anatase phase. This gives short Li
O distances along (Figure 5b), which explains the stability of structures (i)
(iii) as an increased Coulomb interaction. To compensate for the contraction of the lattice around the intercalated Li, the adjacent vacant sites along the lattice direction undergo a compensatory expansion

(Figure 5a), making it unfavorable for these to be occupied by additional Li. Populating pairs of neighboring octahedra along Æ100æ prevents both Li from achieving their optimal coordination geometry, shown in Figure 5b. The presence of common structural subunits in configurations with similar energies implies that the relative arrangement of these Li2O10 units has a small effect on the system energy. Therefore, when considered across large length scales, these subunits are expected to be disordered. This is consistent with the absence of supercell reflections in experimental diffraction data.14 It is straightforward to construct hypothetical structures with lower symmetry that locally appear as (i)
(iii) (Figure 6). Along [001] and [010], this can be achieved by simply combining structures (i)
(iii). We considered an expanded 2  2  2 cell constructed from two layers of structure (i), where the second layer has the Li positions displaced by ((1)/(2),0,0). This can equivalently be thought of as a (i)
(iii)
(i)
(iii) stacking sequence. Even with this high interface density the optimized structure is only 51 meVLi
1 less stable than an equivalent (i)
(i)
(i)
(i) supercell and is thermally accessible under ambient conditions. It is only along Æ100æ that a nonperiodic construction requires the disrupting the Li2O10 octahedral pairs. In this case, it is necessary for adjacent interstitial sites to be either both occupied or both vacant. This requires relatively high-energy local structures such as (iv), and coherence lengths are expected to be greatest along this direction. The calculations described here predict that the origin of the anatase
titanate phase separation is the low energy of specific lithium configurations for x(Li) = 0.5 and not the CJT mechanism of Koudriachova et al.12 At this stoichiometry, a number of low-energy Li configurations exist that are characterized by pairs of occupied interstitial octahedral sites that edge-share in the xz plane. This is a consequence of alternating O
O distances along Æ100æ, which allows all intercalated Li to achieve Coulombically favorable short Li
O distances. Hence intercalated lithium is not randomly distributed among interstitial sites, in contrast with previous suggestions,4,14 Competing arrangements of paired octahedra have similar energies; consequently, no long-ranged order is expected, explaining the apparent contradiction between 1659

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The Journal of Physical Chemistry Letters the local lithium ordering and the absence of supercell reflections in experimental diffraction data.14

’ COMPUTATIONAL METHODS Density functional theory calculations were performed in the plane wave code VASP20,21 using a basis set cutoff of 500 eV. Valence
core interactions were treated with the projectoraugmented wave approach,22 with cores of [Ar] for Ti, [He] for O, and [He] for Li. The gradient-corrected (GGA) exchangecorrelation functional of Perdew et al. was used,23 with selected calculations supplemented with a Dudarev “+U” correction of U = 4.2 eV applied to the Ti d states (GGA+U).24 This U value has been obtained by fitting to experimental data the splitting between occupied and unoccupied Ti d states for oxygen vacancy states at the (110) surface of rutile TiO225 and gives an improved description of Ti 3d states when charge is donated to the host lattice.26
28 In the case of Li-intercalated anatase TiO2, GGA+U correctly predicts the splitting between and occupied Ti3+ defect peak and the unoccupied conduction band states seen in experimental X-ray photoelectron spectra (XPS),16 in contrast with GGA, where donated charge erroneously populates the bottom of the conduction band.29 +U corrected calculations also typically give improved agreement with experiment for lithium intercalation voltages.29,30 k-point sampling used a ((4/nx)  (4/ny)  2) Monkhorst-Pack mesh for each nx  ny  1 supercell. All calculations were spin-polarized. For all geometry optimizations, a series of constant pressure calculations were performed, with the resulting energy
volume data fitted to the Murnaghan equation of state. Average intercalation voltages (intercalation energy per Li) were calculated as [E(LixTiO2)
E(TiO2)
xE(Li(s))] 3 [Fx]
1, where F is the Faraday constant,30 with reference to metallic Li, calculated as a Li2(s) unit cell with 16  16  16 k-point sampling. ’ ASSOCIATED CONTENT

bS

Supporting Information. Cell coordinates for the low energy x(Li) = 0.5 configurations (i)
(iii) are provided in .cif format. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] (B.J.W.). watsong@ tcd.ie (G.W.W.).

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