Electronic band structure and Li diffusion paths in (LaLi)TiO3

Solid State Ionics 177 (2006) 1145 – 1148 www.elsevier.com/locate/ssi

Electronic band structure and Li diffusion paths in (LaLi)TiO3 Shinji Ono a , Yusuke Seki b , Shoji Kashida c,⁎, Michisuke Kobayashi d a

Department of Electrical Engineering, Faculty of Engineering, Doshisha University, 1-3 Miyakodani Tatara, Kyotanabe, Kyoto, 610-0394 Japan b Graduate School of Science and Technology, Niigata University, Ikarashi Ninocho 8050, Niigata, 950-2181, Japan c Department of Environmental Science, Niigata University, Ikarashi Ninocho 8050, Niigata, 950-2181, Japan d Department of Physics, Niigata University, Ikarashi Ninocho 8050, Niigata, 950-2181, Japan Received 14 February 2006; accepted 24 April 2006

Abstract The electronic structure and the Li diffusion paths in the lithium doped lanthanum titanate have been studied. The band dispersion and the density of states (DOS) are calculated using the linear-muffin-tin-orbital (LMTO) method. The model structure used contains La-rich and La deficient layers, with the 2ap × 2ap × 2ap unit cell and base centered C symmetry. The primitive cell contains 20 atoms represented by La3LiTi4O12. The energy contour map, where Li ions are assumed to move within the La-deficient (002) layer, shows that the stable position of Li ions is off centers of the vacant La sites and that Li ions migrate through the bottlenecks at 2c sites surrounded by four oxygen ions. © 2006 Elsevier B.V. All rights reserved. Keywords: Lithium doped lanthanum titanate; Superionic conductors; Electronic structure

1. Introduction ABO3 type lithium doped lanthanum titanates, expressed by the formula La2/3−xLi3xTiO3, have attracted wide interest because of their high Li-ion conductivity and application to rechargeable batteries. A number of studies, including chemical analysis, powder X-ray scattering and electrical conductivity measurements, have been accumulated in order to investigate the mechanism of fast ionic conduction in these compounds [1– 4]. Several structural models have been presented on the basis of powder X-ray diffraction, electron diffraction and electron microscopy data. Almost all models are based on the ordering of La atoms on the perovskite A-site and alternate stuck of La-rich (A1) and La-deficient (A2) layers along the c-axis [2–8]. It was established that in the low Li content (x b 0.06) the crystal has orthorhombic distortion, while in the higher Li content (0.06 b x b 0.14) it has tetragonal symmetry [4]. Detailed electron microscopy studies revealed micro-twin structures, the maximum domain size was found to change from one thousand A2 at the low Li content of x ∼ 0.08 to one hundred A2 at the ⁎ Corresponding author. Tel./fax: +81 25 262 6131. E-mail address: [email protected] (S. Kashida). 0167-2738/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2006.04.030

high Li content of x ∼ 0.11 [5]. For the tetragonal structure, two structure models are proposed, one has the unit cell ap × ap × c (∼2ap), where ap is the ideal cubic perovskite cell parameter [5], and the other with the unit cell 21/2ap × 21/2ap × c(∼ 2ap) [4]. Among the lithium doped lanthanum titanates, La3/2−xLi3xTiO3 (x ∼ 0.05) was found to have the highest ionic conductivity, 1 × 10− 3 Scm− 1 at room temperature [2]. From detailed analysis of the site percolation on Li ion conductivity, the high ionic conduction is ascribed to La vacancies at the A sites, through which Li ions migrate [9,10]. Several model calculations were done in order to simulate the mechanism of the fast ionic conduction in (La, Li)TiO3. Molecular dynamic simulations were reported where the nature of chemical bonds, the static and dynamic properties of the mobile ions, i.e., Li distribution and diffusion process have been analyzed [11,12]. In a recent DV-Xα cluster calculation, the density of states (DOS), bond overlap population and the net charge variation are discussed [13]. In this work, we have studied the electronic structure and DOS of the compound using the linear-muffin-tin-orbital (LMTO) method [14]. From the calculation of the total energy as a function of Li coordinates, the ground-state structure and the Li ionic diffusion paths in (La, Li)TiO3 are discussed.

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2. Calculation methods and the structural model The band calculations are done using the full-potential linear muffin-tin-orbital program LMTART [15], where the local density approximation (LDA) is used. In this calculation, the space is divided into muffin-tin spheres and the interstitial region. Within the muffin-tin spheres, the charge density and potential are expanded using spherical harmonics, and in the interstitial region they are expanded in plane waves. The maximum angular momentum used in the expansion lmax is 6. As the base functions s, p and d orbitals are taken for Li, O and Ti atoms, and f orbital is also taken into account for La atoms. The initial charge density is taken as a superposition of the neutral atomic charge densities. The total energy is estimated as the sum of the following terms: Etotal = Tval + Tcor + Eel + Exc where Tval and Tcor are the kinetic energies of the valence and core electrons and Eel is the electrostatic energy including electron– electron, electron–nucleus and nucleus–nucleus interactions and Exc is the exchange energy. The convergence is assumed if the self-consistent total energy difference between subsequent iterations is less than 0.1 meV. The density of states (DOS) is calculated using the tetrahedron method, where 6 × 6 × 6 division in the k-space is used. Details of the calculation methods are reported in Ref. [15]. The structural model used in this calculation is taken from the powder neutron diffraction data on La0.62Li0.16TiO3 [7,8]. The structure is composed of alternate stuck of La-rich (A1) and La-deficient (A2) layers along the c-axis, and belongs to the orthorhombic space group Cmmm, with a ≈ 2ap, b ≈ 2ap and c ≈ 2ap (cf. Fig. 1). For the La-rich layers, the occupation probability of La is reported 0.95, while for the La-deficient layers, the occupation probability of La is 0.39 and the occupation probability of Li is 0.5. Unfortunately, standard band calculation method is not applicable for such a partially occupied structure. In this calculation, therefore, we take a modified model where in La-deficient (A2) layers only half of the 4j and 4h sites in the Wyckoff notation are occupied by La and Li ions, respectively (see, Fig. 2a and b). The structure has the base centered C symmetry, however, the mmm symmetry is lost, and the primitive cell has a 21/2ap × 21/2 ap × 2ap unit con-

Fig. 2. Atomic arrangements in the (002) plane, where the filled black circles represent Li ions. (a) disorder structure of La0.62Li0.16TiO3 derived from neutron diffraction data [8], (b) ordered structure model of La3LiTi4O12 used in the calculation.

taining 20 atoms. The crystallographic data used for the calculation are summarized in Table 1. 3. Results and discussion 3.1. Band structure and DOS of La3LiTi4O12 The calculated band structure and DOS of La3LiTi4O12 are shown in Figs. 3 and 4. The lowest two bands located around −19 and −17 eV are derived from O 2s and La 5p states, respectively. The main valence bands extending from −7.5 to −2.5 eV are derived mainly from the O 2p states. The lower part of the main valence band is composed of O 2p–Ti 3d and La 5d bonding Table 1 Crystal data of the hypothetical La3Li1Ti2O6 Crystal group

Orthorhombic

Lattice parameter

a = 7.73 A, b = 7.75 A, c = 7.79 A Atom (x, y, z)

Fig. 1. Crystal structure of the lithium doped lanthanum titanate La0.62Li0.16TiO3 [8].

Positional parameters La-1 La-2 Li Ti O-1 O-2 O-3 O-4 O-5

(0.00, 0.25, 0.00) (0.00, 0.25, 0.50) (0.25, 0.00, 0.50) (0.25, 0.00, 0.25) (0.25, 0.00, 0.00) (0.25, 0.00, 0.50) (0.25, 0.25, 0.25) (0.00, 0.00, 0.25) (0.00, 0.50, 0.25)

Wyckoff notation in Cmmm 4i 4j 4h 8o 4g 4h 8m 4k 4l

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lowers the Fermi level, there will be no excess electron and a band gap will appear between the O 2p based valence bands and the Ti 3d based conduction bands. Fig. 3 suggests that the band gap will be situated at Γ and the value is about 2.3 eV. For comparison, we have also calculated the band structure of hypothetical LaLiTi2O6, where another La atom is replaced by a Li ion. As expected, the band gap appears between the O 2p states and the Ti 3d states. A magnetic susceptibility measurement done on LaLiTi2O6 showed that there is no electron in the Ti 3d states [3]. It is in contrast to the case of LaTiO3, which shows a G(1/2,1/2,1/2)-type antiferromagnetic ordering with magnetic moment μ = 0.46μB [17]. 3.2. Fast ionic paths in La3LiTi4O12 In order to search for the stable structure and the Li diffusion paths, we calculate the total energy as a function of Li coordinates. Fig. 5 shows the total energy map where Li ions are assumed to move within the La deficient (002) layer. We assumed the orthorhombic symmetry given in Table 1, and fold back the data to obtain this map. The contour map shows a flat bottom around the vacant La site at (0.5, 0.25, 0.5), however, the real minimum appears at an off center position (0.45,0.15,0.5) and equivalent points, where the energy is lower (∼0.5 eV/Li ion) than that at the center (0.5, 0.25, 0.5). At the minimum point (0.45,0.15,0.5), the distance between Li and O ions is about 1.93 A. The ionic radii of the elements have been studied under various circumstances and the data is tabulated [18]. The Li–O

Fig. 3. The electronic structure of La3LiTi4O12, calculated along the symmetry lines of the Brillouin zone, X(1,0,0)–Γ(0,0,0)–Z(0,0,1/2)–T(0,1,1/2)–Y (0,1,0)–Γ(0,0,0)–R(1/2,1/2,1/2)–S(1/2,1/2,0)–Γ(0,0,0). The energies of the eigenstates are shifted to set the Fermi level to 0 eV.

states and the upper part is the O 2p non-bonding states. The lowest part of the conduction bands above −0.5 eV is the O 2p–Ti 3d anti-bonding states and mainly composed of the Ti 3d orbitals. The flat bands condensed around 2.5 eV are the La 4f states, and the bands from 3 to 6 eV are the La 5d states. The sparse bands from 6 to 10 eV are derived from the Li 2s and 2p states, suggesting that the lithium atom is almost completely ionized. The calculated dispersion (Fig. 3) shows that the Fermi level crosses the conduction bands, suggesting that La3LiTi4O12 is metallic. It is not consistent with the experimental result that (La, Li)TiO3 is an insulator. If we assume the valences of the atoms, La (+3), Li(+1), Ti(+4) and O(−2), there are two excess electrons in La3LiTi4O12. These two electrons are in the conduction bands derived from the Ti 3d states. The end compound, LaTiO3 has attracted wide interest as, charge(valence)–orbital–spin(magnetic) coupled system, and its electronic structure has extensively been studied. LaTiO3 is known as a 3d1 perovskite, in which a simple one-electron band theory gives metallic bands, but owing to the strong on-site Coulomb repulsion, the d-band splits (Eg ∼ 0.2 eV), and LaTiO3 is known to behave as a Mott–Hubbard insulator [16]. As for the lithium doped lanthanum titanates, which we are concerned here, the chemical formula La2/3−3xLi3x□1/3−2xTiO3 is usually used, where □ means cation vacancy. If the cation vacancy

Fig. 4. Calculated partial DOS for La3LiTi4O12.

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fashion. In the real system, the diffusion of a Li ion takes place from a vacant La site to neighboring vacant La site through the saddle point. In the present small-scale model containing 20 atoms, there is no pathway connecting between vacant La sites. In order to reproduce the experimental threshold energy, therefore, a more large scale model is necessary. In conclusion, in this work we have investigated the electronic structure and DOS in the lithium doped lanthanum titanates. The calculated total energy as a function of Li coordination is in accord with the recent molecular dynamic simulation, which showed that Li ions occupy off center positions near the vacant La sites and migrate through the bottle neck at 2c sites [12]. References

Fig. 5. Contour map of the total energy calculated over the displacements of Li ions within the (002) plane, where the orthorhombic symmetry (Table 1) is assumed and the data are fold back to have tetragonal symmetry. The minima appear around (0.45,0.15,0.5) and equivalent positions. The four corner sites are occupied by oxygen ions.

distance is close to the sum of the known ionic radii, Li1+(0.59 A) and O2−(1.35 A), each for four and two coordination, respectively. The distance between La and O ions is 2.74 A, which is close to the sum of the reported ionic radii, La3+(1.36 A) for twelve coordination and O2−(1.35 A). The replaced Li ion occupies a fairly large space because of the ionic size difference, La3+(1.03 A) and Li1+(0.76 A) for six coordination. This would allow the Li ion, driven by the electrostatic Madelung energy, occupy the off center positions. Fig. 5 also shows that the saddle point of the Li diffusion path is located at 2c (0.5,0,0.5) site, where the Li ion is surrounded by four oxygen ions and the energy is higher (∼ 0.7 eV/ Li ion) than that at the center (0.5, 0.25, 0.5). The activation energy for a Li ion to overpass the saddle point is, therefore, around 1.2 eV. In the present model, the Coulomb repulsion between the Li and the nearby La ions makes the threshold energy too high compared with the experimental value of 0.2– 0.4 eV [2]. In this calculation, we treat cooperative motions, i.e., all Li ions are assumed to move simultaneously in the same

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