Computational Study of Lithium Titanate as a Possible Cathode

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Computational Study of Lithium Titanate as a Possible Cathode Material for Solid-state Lithium-sulphur Batteries Valery Weber, Teodoro Laino, Alessandro Curioni, Thomas Eckl, Christine Engel, Jitti Kasemchainan, and Nils Salingue J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp5105455 • Publication Date (Web): 08 Apr 2015 Downloaded from http://pubs.acs.org on April 13, 2015

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The Journal of Physical Chemistry

Computational Study of Lithium Titanate as a Possible Cathode Material for Solid-State Lithium-Sulphur Batteries Valéry Weber,† Teodoro Laino,∗,† Alessandro Curioni,† Thomas Eckl,‡ Christine Engel,‡ Jitti Kasemchainan,‡ and Nils Salingue‡ IBM Research – Zurich, Säumerstrasse 4, CH-8803 R¨ uschlikon, Switzerland, and Robert Bosch GmbH, Corporate Research and Advance Engineering, Robert-Bosch-Platz 1, 70839 Gerlingen, Germany E-mail: [email protected] Phone: +41 (0) 44 724 8933. Fax: +41 (0) 44 724 8958

∗

To whom correspondence should be addressed IBM Research – Zurich ‡ Robert Bosch GmbH †

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Abstract LiS cells are currently built with metallic lithium as anode, a liquid electrolyte and a cathode composed of a mixture of sulphur, carbon, and binder. While this type of cell produces good capacity during the early cycles, unwanted reactions with the electrolyte degrade the cathode and anode, making the whole cell not competitive with Li-ion batteries. A viable solution to mitigate this problem is the replacement of the carbon, binder and electrolyte with a ceramic matrix, with high electronic and ionic conductivity. Lithium titanate (Li4 Ti5 O12 ) spinel may be a potential candidate for the fabrication of composite cathodes, due to its mechanical robustness and its high electronic and Li-ion conductivity. In this manuscript, we present an ab initio molecular dynamics study complemented with experimental investigations, offering a novel interpretation for the Li-ion mobility in Li4 Ti5 O12 and Li7 Ti5 O12 as well as for the chemical reactivity of these materials with molecular sulphur. Finally, we studied the passivation of Li4 Ti5 O12 and Li7 Ti5 O12 surfaces by lithium carbonate, studying both Li-on mobility at the interface and sulphur reactivity. Based on our results, the deployment of Li4 Ti5 O12 and Li7 Ti5 O12 materials for sulphur-based battery technology is questioned mainly by the lower Li-ion conductivity of the carbonate-passivated surfaces and by the chemical reactivity of Li7 Ti5 O12 with sulphur molecules, which would lead to self discharge, with resulting loss of capacity and inferior battery performance.

Keywords Lithium–Sulphur, Batteries, Lithium Titanate, Lithium ion mobility, Chemical degradation

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relative arrangement of titanium and lithium atoms is unknown. The

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16d

[Li1/3 Ti5/3 ]32e O4

framework is very stable, with face-shared tetrahedral (8a) and octahedral (16c) interstitial Li-ion positions in the lattice, which provides a three-dimensional network of connections for Li-ion migration. In the Li4 Ti5 O12 spinel cubic unit cell, the tetrahedral (8a) sites are occupied by Li atoms, whereas the octahedral (16c) sites are empty, and the structure is denoted as

8a

[Li]16d [Li1/3 Ti5/3 ]32e O4 . 2 At the end of the intercalation process, one lithium is

added into the lattice and located at the octahedral (16c) sites. At the same time, lithium initially located at the tetrahedral (8a) sites relocates to the octahedral (16c) sites. This structure is denoted as

16c

[Li2 ]16d [Li1/3 Ti5/3 ]32e O4 . The stable spinel framework and the zero-

strain insertion property, 2 peculiar to this material, enable the reversibility during cycling, which is important for battery applications: 8a

[Li]16d [Li1/3 Ti5/3 ]32e O4 + Li+ + e– ↔

16c

[Li2 ]16d [Li1/3 Ti5/3 ]32e O4

Many studies on Li4 Ti5 O12 , most of which are experimental, focused on the electronic and ionic conductivity, 3–10 being these properties extremely important for electrode materials in Li-ion batteries. In summary, the insulating nature of Li4 Ti5 O12 causes its intrinsic electronic conductivity to be very low, while chrono-amperometric measurements have shown that the chemical diffusion coefficient of Li+ in Li4 Ti5 O12 is in the range of 10−9 cm2 /s to 10−13 cm2 /s. 11 With alternating current impedance studies and lattice gas model based Monte Carlo simulations, Jung 12 confirmed the two phase co-existence state of Li-poor and Li-rich phases during the charge/discharge process. Recently, we measured the electronic (σ elec ranging from 2 × 10−11 to 2 × 10−8 S/cm), and ionic (σ ionic ranging from 1 × 10−8 to 2 × 10−7 S/cm) conductivities of Li4 Ti5 O12 at room temperature. We conducted galvanostatic intermittent titration technique (GITT) measurements to determine the true ion diffusion coefficient for the Li4 Ti5 O12 , which provided a diffusion coefficient of 10−12 cm2 /s for Li+ . Similarly, we also measured the electronic conductivity for a Li-rich Li4 Ti5 O12 phase (Li4+x Ti5 O12 , where x is unknown) in which we do not entirely control the stoichiometry of enriched Li-ions, obtaining values in the range from 4


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6 × 10−6 to 6 × 10−3 S/cm. The ionic conductivity of the Li-rich phase is approximately 7 × 10−5 S/cm. The rather high range (up to 3 order of magnitude) of measured conductivity values can be justified by different preparation conditions, which can affect the grain boundaries, porosities and secondary phases with strong variations in terms of conductivity measurements. Although many investigations have been performed on Li4 Ti5 O12 , 3–10,13–17 some important properties still are not clear from the published literature. For instance, many experiments have shown that the volume varies slightly with Li in/out of the [Li1/3 Ti5/3 ]O4 framework, but their results differ from each other on whether the lattice expands or shrinks when Li ions are inserted. Some X-ray diffraction measurements supported the idea that the cubic unit cell expands a little upon Li insertion. 2,18 On the other hand, other X-ray diffraction measurement 19 and neutron diffraction data 20 showed that the cubic unit cell shrinks a little when Li ions are inserted. We also conducted X-ray diffraction (XRD) measurements of both Li4 Ti5 O12 and Li7 Ti5 O12 , obtaining lattice parameters of 8.3595 ˚ A and 8.3538 ˚ A for the Li4 Ti5 O12 and Li7 Ti5 O12 , 21 respectively. Moreover, the mechanism of ionic conductivity is not entirely clear, and, most important for potential LiS solid-state batteries, the type of reactivity of the surfaces of lithium titanate spinels with sulphur (S8 ) molecules has never been investigated. In the present work, we focus on the bulk Li-ion mobility and on the surface reactivity of molecular sulphur (S8 ) on both Li4 Ti5 O12 and Li7 Ti5 O12 by means of ab initio molecular dynamics simulations. Moreover, we modelled a Li2 CO3 -passivated surface of Li4 Ti5 O12 and Li7 Ti5 O12 , to study the impact on the mobility of Li-ions at the interface of both Li4 Ti5 O12 – Li2 CO3 and Li7 Ti5 O12 –Li2 CO3 as well as on the reactivity of S8 on the Li2 CO3 surface. The remainder of this paper is divided into three major sections: Methods, in which we report the computational setup and validation on both Li4 Ti5 O12 and Li7 Ti5 O12 , comparing, whenever possible, with available experimental data; Results and Discussion, in which we present our findings on the Li-ion mobility for bulk systems (pristine and passivated ones)

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and on the chemical reactivity of S8 with their surfaces, and Conclusions.

Methods All simulations were performed using the publicly available CP2K code. 22 The CP2K code uses the Gaussian plane-wave method 22,23 based on the Kohn–Sham formulation of density functional theory together with a hybrid Gaussian and plane-wave basis. The normconserving pseudopotentials of Goedecker–Teter–Hutter 24,25 (GTH) and a double–ζ valance basis set augmented with a set of d-type or p-type polarization functions (DZVP) were used throughout. A 400 Ry cutoff for the auxiliary plane-wave grid was employed, and the efficient and numerically stable orbital transformation energy minimizer 26 is used to converge the SCF iterations to 10−6 a.u. of the Born–Oppenheimer surface. The nuclei are propagated by the velocity Verlet 27 algorithm during molecular dynamics simulations. Standard masses are used for all atoms. During atomic position and cell relaxations, the forces are converged to 10−3 Hartree/Bohr. The electronic structure was solved using the PBE 28 generalized gradient approximations to density functional theory. The k-point sampling was limited to the Γ-point. For Li7 Ti5 O12 , because of the limited sampling to the Γ-point only, we performed geometry and cell relaxation using also a 3 × 3 × 3 supercell. Our first goal was to set up a realistic representation of the lithium titanate material as used in lithium-sulphur batteries experiments. We used a 3 × 1 × 1 supercell for structure optimization, while for mobility and reactivity studies we enlarged the structure to 3 × 2 × 2.

System Setup and Validation To satisfy the stoichiometry of Li4 Ti5 O12 , a supercell model containing at least 3 unit cells is required. For initial system setup, we used a configuration of 3 × 1 × 1. As the 16d sites are randomly occupied by one-sixth (1/6) lithium and five-sixths (5/6) titanium, it is necessary to determine the most favorable arrangement of Li and Ti atoms at the 16d

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site to obtain a reasonable bulk model. However, with such a large supercell, it is too demanding to try all possible distributions of these atoms. Therefore, our strategy focused on optimizing the distribution of the Li and Ti atoms over the large supercell, testing four different random configurations. For each of these configurations, we performed a 10 ps long molecular dynamics (MD) run with an NPT ensemble, 29 using a temperature of 300 K, a pressure of 1 atm and an integration time step of 1 fs. We report in Table 1 the averages of the cubic lattice parameter and of the potential energy, which provides a measure of the difference of the average potential energy for these configurations with respect to the most stable one. The model with the lowest energy is identified as the structure Li4 –4 (see Table 1). The four different structures give lattice parameters that are within 0.04 ˚ A. Table 1: Lattice parameters and average potential energies (shifted to the lowest value) for the 4 different Li4 Ti5 O12 structures tested. Structure Li4 –1 Li4 –2 Li4 –3 Li4 –4

Lattice parameter [˚ A] 8.48 ± 0.02 8.44 ± 0.01 8.47 ± 0.01 8.45 ± 0.01

Avg. potential energy [Hartree] 0.233 ± 0.015 0.038 ± 0.015 0.120 ± 0.015 0.000 ± 0.015

A supercell model of Li7 Ti5 O12 is constructed by removing all Li atoms from the 8a sites and adding 16 Li atoms to the 16c sites of the Li4 Ti5 O12 supercell model. Similar to the protocol followed for Li4 Ti5 O12 , we built four different structures with different lithium ion positions, denoting the corresponding models as Li7 –1, ..., Li7 –4, and performed an MD run with similar conditions as those for Li4 Ti5 O12 (see Table 2). To account for the metallic properties and the limited sampling to the Γ-point only, we used for geometry and cell relaxation also a larger supercell (3 × 3 × 3). In the following, the calculations are performed with the Li4 –4 and the Li7 –2 models, which are the ones with the higher cohesive energies and therefore considered to be the most stable ones. The different structures yield lattice parameters that are within 0.01 ˚ A. The error in using a small supercell for Li7 Ti5 O12 , rather

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than a large one, was smaller than 0.1%. Table 2: Lattice parameters and average potential energies (shifted to the lowest value) for the 4 different Li7 Ti5 O12 structures. Structure Li7 –1 Li7 –2 Li7 –3 Li7 –4

Lattice parameter [˚ A] 8.30 ± 0.01 8.29 ± 0.01 8.29 ± 0.02 8.29 ± 0.01

Avg. potential energy [Hartree] 0.026 ± 0.015 0.000 ± 0.015 0.020 ± 0.015 0.022 ± 0.015

Lattice parameters The good cycling performance of the Li4 Ti5 O12 material is mainly attributed to the stability of the [Li1/3 Ti5/3 ]O4 framework and to the small volume changes during cycling. 1 As mentioned above, the volume changes very slightly with Li in/out of the [Li1/3 Ti5/3 ]O4 framework, and the experimental observations differ from each other on whether the lattice expands or shrinks during the intercalation process. In the present study, the theoretically optimized lattice constants are shown in Table 1 and Table 2. For the Li4 –4 and Li7 –2, structures we obtained a value of 8.45 ± 0.02 ˚ A and 8.29 ± 0.01 ˚ A for Li4 Ti5 O12 and Li7 Ti5 O12 , respectively. These theoretical values, specifically with regard to Li4 Ti5 O12 , are in extremely good agreement with experimental results. 2,18–20 The calculated lattice constants are reasonable, as it is known that GGA functionals often overestimate the absolute lattice constant by several percent while still performing very accurately when comparing relative values. The theoretical results show that the lattice tends to shrink by 2 to 3 % after lithium atoms have been intercalated. The reduced lattice constant is mainly attributed to the change of the Li positions from the 8a sites to the 16c sites. The atoms in the Li7 Ti5 O12 lattice are arranged in a NaCl-like (rock-salt) structure, in which the atoms are ordered in a more compact way than in the Li4 Ti5 O12 lattice. Of the various experiments, some X-ray diffraction measurements supported that the cu-

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bic unit cell expands a little after Li insertion into the lattice, and then recovers to the initial state after the inserted Li ions are electrochemically extracted. 2,18 On the other hand, other researchers have shown, through X-ray diffraction measurement 19 and neutron diffraction measurement, 20 that the cubic unit cell shrinks a little when Li ions are inserted. As the lattice changes only very slightly, the consistency of experimental and theoretical measurements is a delicate issue. Given the trend observed in our calculations and reported by other studies, 8 we can conclude that there is minor contraction of the lattice cell parameters upon lithiation. Electronic structure Recently, Liu et al. 30 studied the electronic structure of Li4 Ti5 O12 and the effect of Ti-site transition metal doping on the electronic structure using first principles calculations. In both cases, the cubic spinel models do not satisfy the Li4 Ti5 O12 stoichiometry, and the calculated electronic structures are metallic. A reasonable model to represent the Li4 Ti5 O12 stoichiometry requires a large supercell. The electronic structure of Li4 Ti5 O12 is insulating, and the band gap opens between the occupied O–2p states and the empty Ti–3d states. Fig. 2 shows the calculated projected density of states (PDOS) of Li4 Ti5 O12 for the Li4 –4 model. The highest occupied state is shown as dashed line and is mostly composed of the O–2p states. The width of the valence band is about 5 eV and the conduction band, made by contribution of the Ti–3d and O–3d states, starts 2 eV above the valence band. After intercalating metallic lithium atoms into the lattice of Li4 Ti5 O12 , extra electrons are brought into the unit cell. These electrons tend to occupy the Ti–3d states, and the Fermi level is shifted up to the conduction band, which makes the system metallic. This electron transfer decreases the average oxidation state of the titanium ions from 4+ to 3.4+. In Fig. 3, we can observe that the Fermi level lies within the middle of the conduction band. The metallic characteristic of the electronic structure shows that the electronic conductivity

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Figure 2: Projected density of states for Li4 Ti5 O12 . The dashed line indicates the energy of the highest occupied state.

of Li7 Ti5 O12 is much higher than that of the insulating Li4 Ti5 O12 , which is also observed experimentally (see e.g. 31 ).

Figure 3: Projected density of states for Li7 Ti5 O12 . The dashed line indicates the energy of the highest occupied state.

The partially filled Ti–3d orbitals create an extremely complex landscape for the description of the electronic wave function. Also, a large number of high-spin states can be found in a narrow window of energy.

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IR characterization for Li4 Ti5 O12 To have a further validation of the bulk material, we computed IR spectra for the Li4 –4 model. The vibrational spectra were computed by Fourier transform of the dipole moment autocorrelation function. The results are shown in Fig. 4, where we also provide the experimental spectrum as determined by Pecharromán and Amarilla. 15 The computed IR spectrum is slightly red-shifted compared to the experimental data, as expected from GGA calculations, with most of the features between 200 and 700 cm−1 well reproduced.

Figure 4: IR spectrum for Li4 Ti5 O12 (structure Li4 –4), experimental 15 at 298 K (black line) and simulation at 300 K (blue line).

Surface formation energies To inspect the chemical stability of lithium titanate spinel and rocksalt modifications versus molecular sulphur (S8 ), we first characterized the different surfaces. The slabs were cut from the crystal along the corresponding crystallographic planes and the termination of Ti ions was balanced (between the two different surfaces) with the constraint of maintaining the proper stoichiometry, while minimizing the dipole of the slab. As no experimental information was available on the stability of the different surfaces, we computed the surface formation energy of Li4 Ti5 O12 for the low Miller indexes (100), (110) and (111), which we report in Table 3. For the (111) surfaces we also attempted a recently proposed reconstruction model, 32 11



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which proved to be unsuccessful for this complex material, casting serious doubts on the general applicability of this protocol. We observe that the (100) surface has a smaller surface Table 3: Low Miller indexes surface formation energies for Li4 Ti5 O12 . Surface (100) (110) (111)

Surface formation energy (J/m2 ) 1.01 1.59 1.70

formation energy and is to be considered the most abundant one of the three considered. In a similar way, we characterised the surface formation energy for Li7 Ti5 O12 and the three different Miller index. The formation energies are reported in Table 4. Table 4: Low Miller index surface formation energies for Li7 Ti5 O12 Surface (100) (110) (111)

Surface formation energy (J/m2 ) 0.79 1.64 1.69

As for Li4 Ti5 O12 , the (100) surfaces has the smallest surface formation energy. In Fig. 5, we present the structure of the different surfaces for Li4 Ti5 O12 and Li7 Ti5 O12 . While our calculations allows us to affirm that the (100) surface is the lowest in energy (most stable and therefore most abundant), it is also clear that a critical analysis of the results of the surface formation energies shows that there is no predominant surface. In fact, depending on the chemical potential of Lithium, Titanium and Oxygen, we expect different relative stabilities. Therefore, it is reasonable to assume that the surface of the grain material may be a coexistence of different surface types as outlines in few recent works, 33,34 in which, by using peculiar synthetic conditions, either surfaces (110) 33 or (111) 34 were shown to be the most predominant. For this reason, we will report the reactivity for all three surfaces in the next section. 12


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Figure 5: Structure of the different surfaces for Li4 Ti5 O12 (upper panel) and Li7 Ti5 O12 (lower panel). Oxygen atoms are shown in red, lithium atoms in pink and titanium atoms in blue.

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Results and Discussion In this section, we discuss the findings on the lithium-ion mobility in Li4 Ti5 O12 and Li7 Ti5 O12 bulk and at the interface of the Li2 CO3 -passivated material. In the last part, we discuss the reactivity of the surfaces of these two materials with molecular sulphur.

Li-ion mobility In Li4 Ti5 O12 , the Li ions reside preferentially in two crystallographically distinct sites, viz. in tetrahedrally coordinated 8a sites and in octahedrally coordinated 16d sites. Lithium and titanium ions randomly occupy the octahedral positions 16d, whereas the 8a positions are only occupied by Li ions according to the spinel notation

8a

[Li]16d [Li1/3 Ti5/3 ]32e O4 . Li ions on

the 8a position can migrate to an empty tetrahedral position via the 16c octahedra connected to two 8a tetrahedra by face sharing. The octahedra 16c and 16d share common faces with the tetrahedron 48f. Thus, in addition to the diffusion pathway 8a - 16c - 8a, Li ions can migrate using the path 8a - 16c - 48f - 16d and vice versa. They can also hop directly between 16c and 16d sites and/or 8a and 48f positions. The involvement of tetrahedral 8b sites in the diffusion process is less probable. A number of studies have focused on the electrochemical behavior of Li insertion into and Li diffusion in the Li intercalated material, but only few investigations about low-temperature Li dynamics in the non-intercalated host material Li4 Ti5 O12 have so far been reported. Recently, Wilkening et al. 9 published a work on Li diffusion in purephase micro-crystalline Li4 Ti5 O12 with an average particle size in the millimeter range. They employed 7 Li solid-state NMR spectroscopy using spin-alignment echo (SAE) and spin– lattice relaxation (SLR) measurements, and reported extremely slow Li jump rates between T = 295 K and 400 K. Values of t−1 ranging from 1 s−1 to about 2200 s−1 were directly measured by recording the decay of spin-alignment echoes as a function of the mixing time and constant evolution time. Their results pointed out that the slow Li diffusion in nonintercalated Li4 Ti5 O12 · t−1 (1/T ) follows an Arrhenius behavior with an activation energy

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of about 0.86 eV. Interestingly, the results of Wilkening et al., 9 obtained by means of NMR spectroscopy, are comparable to activation energies deduced from conductivity measurements (0.94(1) eV) 9 and from SLR measurements in the rotating frame (0.74(2) eV) 9 rather than to those performed in the laboratory frame, EA(low-T ) = 0.26(1) eV at low T . 9 Noticing that this value is much smaller than that obtained by SAE-NMR, Wilkening et al. 9 offer a justification of this discrepancy by saying that it is well known that the slope of the low-temperature flank of the peak T1−1 (1/T ) can be influenced by correlation effects such as Coulomb interactions and/or structural disorder. Moreover, low-temperature spin-lattice relaxation rates are governed by short-range and/or local (within-site) Li motions with low activation energies rather than by long-range Li diffusion which, however, is expected to be probed by echo NMR techniques. Therefore, the value of 0.26(1) eV should be correlated to some short-range Li-ion mobility event. To understand and clarify this issue, we investigated the mobility of Li ions in both Li4 Ti5 O12 and Li7 Ti5 O12 by looking at the Li-ion mobility induced by Li vacancies inside the spinel material along the diffusion pathway 8a - 16c - 8a. Mobility induced by the presence of Li vacancies For the mobility study, we considered a larger system (767 atoms) [3 × 2 × 2] to minimize the interaction energy of the defective position between the periodic replica. We created defects, in both the Li4 Ti5 O12 and Li7 Ti5 O12 models, by removing lithium atoms in different positions of a single [3×1×1] unit (49 possible configurations). Starting from these defective structures, we computed the minimum energy paths connecting the motion of the neighboring lithium atoms into the corresponding defect along the diffusion pathway 8a - 16c - 8a. Given the complexity and size of the material, we performed different calculations to obtain statistically meaningful results, providing an average of the barriers in the different Li-ion conduction paths. By performing these averages, we were also able to provide a measure of the thermodynamic stability of the defects and of the kinetic factor by averaging over

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different conductivity paths. The interesting point is that the conductivity of Li ions has an extremely complex landscape. Owing to the random distribution of lithium and titanium atoms, the positions of the defects are all non-equivalent. For example, Li4 Ti5 O12 was characterized by vacancies spanning an energy range of 1.1 eV. In Fig. 6, we show the energy distribution of all possible defects in Li4 Ti5 O12 . As one can see, all defects in Li4 Ti5 O12 can be divided into four distinct bands. By averaging different mobility events, we determined a barrier of approx. 0.3 eV, thus providing an upper limit range of 1.0 eV to 1.4 eV for the conductivity barriers (considering, respectively, the smallest and the largest energy difference between the two lower and upper conductive bands). Our findings offer an explanation for the contradictory experimental measurements: in fact, assuming both the starting and the ending point to lie within the same band (i.e., they differ by 0.1–0.2 eV), this would correspond to an observed barrier of much lower magnitude than if the starting and the ending point were in different bands. This is in agreement with the justification provided by Wilkening et al., 9 as defects in the same band are located close to each other in the crystal structure. Therefore, the small activation energy of 0.26 eV is definitely to be attributed to a short-range motion of lithium atoms. On the other hand, the upper limit of 1.0–1.4 eV compares well with the values determined experimentally (0.94 eV).

Figure 6: Distribution of defects in Li4 Ti5 O12 . The red arrow shows the amplitude of the defect range in Li7 Ti5 O12 (see Fig. 7).

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In contrast to Li4 Ti5 O12 , vacancies in Li7 Ti5 O12 span an energy range of less than 0.5 eV (see Fig. 6 and Fig. 7), all grouped into a single band. By optimizing different minimum energy paths, we derived an average barrier for the Li-ion mobility of 0.6 eV, thus providing an upper limit range of 0.6 eV to 1.1 eV for the conductivity barriers. Including the thermodynamic stability of both vacancies and barriers, the Li-ion mobility in Li7 Ti5 O12 is energetically more favorable than the Li-ion mobility in Li4 Ti5 O12 . To the best of our knowledge, there are no experimental values to compare the Li7 Ti5 O12 results.

Figure 7: Distribution of defects in Li7 Ti5 O12

Passivation by Li2 CO3 In a recent paper, 17 a study on the surface chemistry of the lithium titanate spinel was reported. The surface was found to contain isolated and hydrogen-bonded TiOH groups. In addition, the reaction of gaseous CO2 with the Li+ ions resulted in the formation of surface carbonate ions. In fact, by diffuse reflectance infrared Fourier transform spectroscopy (DRIFT), sharp peaks were identified at 1513 and 1453 cm−1 , with a shoulder at 1380 cm−1 . These bands are not removed by heating to 150 ◦ C and, by comparison to known compounds, are assigned to carbonate ions. Carbonates form via the reaction of CO2 on TiO2 , but these bands are located at different wave numbers and much weaker than the bands observed by Snyder et al. 17 Therefore, Snyder et al. 17 associate carbonates on lithium titanate spinels

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with the Li+ cations, as it is well known that Li2 O readily reacts with CO2 to form lithium carbonate. We performed additional investigation, characterising the surface composition of lithium titanate spinel samples by means of XPS (X-Ray Photoelectron Spectroscopy). We sintered the material at 950 ◦ C for 10 h in air, we polished the surface with sandpaper and stored different samples for 24 hours in ambient atmosphere and in an argon filled glove box respectively. Among others, different carbon and oxygen binding states were detected at the top 5 nm of the samples. The amount of the binding state of carbon at 289.8 eV and of oxygen at 531.4 eV, both assigned to carbonate, are significantly increased for the samples stored in air, compared to those stored in argon, confirming the presence of lithium carbonate on the surface of the lithium titanate spinel after air contact. Therefore, it was crucial to build a novel realistic model: a Li4 Ti5 O12 surface passivated by Li2 CO3 . Ab initio Li2 CO3 slab optimisations have been recently described in literature, 35 with the most stable surface reported to be the (001) and the least stable the (110). However, the passivation process is a complex phenomena that involves the presence of oxygen, water and carbon dioxide and for this reason it is reasonable to expect that the interface between the titanate spinel and the carbonate will be relatively amorphous in nature. For this reason, we decided to investigate the passivation by Li2 CO3 analysing both the (001) and the (110) surface, so to cover the two extremes in surface formation energy for Li2 CO3 . First, we constructed a model for both the least and the most stable Li2 CO3 surface ( (110) and (001), respectively), with lattice cell parameters compatible to those of Li4 Ti5 O12 . At this stage, we considered three layers of Li2 CO3 for a total of 1152 atoms for both surface and and a length of 76 ˚ A ×8 ˚ A (l × d), see Fig. 8. Note that it was quite difficult to estimate the coverage and the depth of the Li2 CO3 passivation layer from experimental measurements, therefore we considered the maximum size, which allowed us to perform reactivity and mobility simulations within a reasonable elapsed time. We placed the Li2 CO3 (110) and (001) on the Li4 Ti5 O12 (100) surface and performed a full scan of the mutual

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should be quite high. In contrast, the hopping process between large open channels is less likely to occur (having an activation barrier of 0.6 eV). Because the mobility in Li2 CO3 was already characterized, we proceeded with the study of the Li-ion mobility at the interface between Li4 Ti5 O12 and Li2 CO3 (for both surfaces). This interface is extremely complex, with a periodicity of almost 80 ˚ A. A full exploration is therefore quite demanding in terms of computational resources. Therefore, we decided to sample a few sites, looking at the diffusion process of a few lithium atom vacancies at the interface between the first layers of Li2 CO3 and the first layers of Li4 Ti5 O12 ( Fig. 10). For

Figure 10: Examples of possible migration paths considered in our mobility studies at the interface. In the upper part, lithium carbonate is depicted (O atoms in red, C atoms in blue, and Li atoms in pink). In the lower part, Li4 Ti5 O12 is depicted (O atoms in red, Ti atoms in blue, and Li atoms in pink). The yellow tube shows an example of a mobility path inside Li4 Ti5 O12 , while the white and green tubes show two examples of mobility paths at the interface between Li4 Ti5 O12 and Li2 CO3 .

the Li4 Ti5 O12 -passivated surfaces, we computed barriers of 0.65 eV on average for Li-ion mobility from Li4 Ti5 O12 into Li2 CO3 (similar values were found for both Li2 CO3 surfaces). For Li7 Ti5 O12 , in contrast we noticed an increase of the barrier up to 0.85 eV from Li7 Ti5 O12 into Li2 CO3 . The increase of the energy barrier for both materials (Li4 Ti5 O12 and Li7 Ti5 O12 ) 20


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clearly indicates a reduced Li-ion mobility at the interface.

Reactivity Understanding the chemical stability of the cell components with the electrolyte is a relevant aspect 38,39 in the battery optimisation process.To study the reactivity of the different surfaces with the cathode material, a sulphur molecule is placed on the top of the atoms that are most exposed to the surface. A full relaxation of the atomic positions is performed for all those configurations. The binding energies are evaluated as the difference between the product and the reactants. In the following, the two sides of the surface are labeled as a “+” or a “–”. Reactivity of molecular sulphur on Li4 Ti5 O12 In this section, we report the findings for the reactivity of molecular sulphur on the Li4 Ti5 O12 surface. The binding energies for the (100) surface range from −9.6 to −165.7 kJ/mol ( Fig. 11, left graph). Molecular sulphur interacts strongly with titanium atoms via 1 or 2 “bonds” (i.e. S8 –Ti or Ti–S8 –Ti). An example of the reactivity is shown in Fig. 12 (top image). In all cases, the sulphur keeps its cyclic structure. The binding energies for the (110) surface range from −68.6 to −471.5 kJ/mol ( Fig. 11 middle graph). Similarly to the (100) surface, the molecular sulphur interacts also for the (110) surface with titanium atoms and in some cases with oxygen atoms, via 1 or 2 “bonds”. While the sulphur breaks its cyclic structure for the + surface in some cases, it remains intact for the – side. An example of the reactivity is shown in Fig. 12 (middle image). The binding energies for the (111) surface range from −34.7 to −1275 kJ/mol ( Fig. 11 right graph). The molecular sulphur binds mostly on titanium atoms, via 1, 2 or 3 “bonds” for the – surfaces, and to titanium and oxygen atoms for the + side. In most of cases, the sulphur breaks up its cyclic structure into one or more fragments for both sides. An example of the reactivity is shown in Fig. 12 (bottom image). 21




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The reaction of the sulphur mostly occurs on the titanium atom present at the surface, and the “reaction” energy can be correlated with the number of oxygen surrounding the reactive site (TiO5 (100) < TiO4 (110) < TiO3 (111)). In some cases, we could observe the molecular sulphur binding to surface oxygens (see, for instance, surface (110) in Fig. 12). The increase of reactivity at the Ti site (and most probably at the O side too) induces stronger electron transfer when S8 reacts. The lithium-rich surfaces (Li7 Ti5 O12 ) show a large increase in the reactivity compared with their lithium-poor counterparts (Li4 Ti5 O12 ) (e.g., up to 840 kJ/mol for the (100) surfaces). This increase in reactivity stems from the small electronic band gap of the lithium-rich systems. Regarding the Li7 Ti5 O12 -passivated surface, we can observed that the Li2 CO3 layer annihilates the reactivity with the molecular sulphur of the clean Li7 Ti5 O12 . The passivated lithium-poor counterpart does not exhibit any reactivity with sulphur. In addition, we note that if molecular sulfur does not ”spontaneously” degrade in presence of the passivated layers, it is because the degraded products are thermodynamical unfavourable.

Conclusions In this work, we studied the bulk Li-ion mobility and the reactivity of molecular sulphur (S8 ) on both Li4 Ti5 O12 and Li7 Ti5 O12 surfaces by means of ab initio molecular dynamics simulations. Inspired by recent experimental findings, we proceeded with the modeling of a surface of Li4 Ti5 O12 and Li7 Ti5 O12 passivated by Li2 CO3 . On this passivated model, we studied both the mobility of Li-ions at the interface of Li4 Ti5 O12 –Li2 CO3 and Li7 Ti5 O12 – Li2 CO3 and the reactivity of S8 on the Li2 CO3 surface. We found that the mobility of Li-ions in Li4 Ti5 O12 is characterized by a complex landscape, whose minima and maxima span an energy range of at most 1.4 eV. Similarly to

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Li4 Ti5 O12 , Li7 Ti5 O12 shows a complex landscape for Li-ion migration, although the energy range spanned along the Li-ion motion is smaller in magnitude than in Li4 Ti5 O12 and of at most 1.1 eV. Regarding the reactivity of molecular sulphur, we characterized the Li7 Ti5 O12 surfaces as more ”reactive” to sulphur than their Li4 Ti5 O12 counterparts. We show that the sulphur molecule reacts mainly with the titanium atoms. The differences in reactivity come from differences in the environment of the titanium atoms and from the available electrons on titanium after lithiation. In fact, a different manifold of TiO5 , TiO4 and TiO3 is produced along the cutting planes of the surfaces, in which the reactivity of each titanium atoms strongly depends on the oxygen coordination. Finally, we studied the passivation of Li4 Ti5 O12 and Li7 Ti5 O12 surfaces by lithium carbonate, finding that it attenuates any type of chemical reactivity. Moreover, the mobility of Li-ions in Li2 CO3 and at the lithium interface with the carbonate is characterized by barriers larger than the ones of the spinel. Therefore it is plausible to assume that, in the presence of a carbonate passivation layer, lithium ions experience a stronger resistance when flowing from the lithium-titanate matrix (through the carbonate) to the sulphur molecules during the discharging/recharging cycles of an hypothetical lithium–sulphur electrochemical solid-state cell. Based on these results, the usage of Li4 Ti5 O12 and Li7 Ti5 O12 in sulphur-batteries is prevented mainly by the lower Li-ion conductivity for the carbonate-passivated surfaces and by the chemical reactivity of Li7 Ti5 O12 with sulphur molecules, which would lead to self discharge, with resulting loss of capacity and inferior battery performance. Further investigations will be needed to find viable solutions before such materials can be efficiently used for sulphur-based battery applications.

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Computational Study of Lithium Titanate as a Possible Cathode

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