Variation in surface energy and reduction drive of a metal oxide lithium-ion anode with stoichiometry: a DFT study of lithium titanate spinel surfaces

Li4Ti5O12 is a “zero-strain” lithium-ion anode material that shows excellent stability over repeated lithium insertion–extraction cycles. Although lithium (de)intercalation in the bulk material has been well characterised, our understanding of surface atomic-scale-structure and the relationship with electrochemical behaviour is incomplete. To address this, we have modelled the Li4Ti5O12 (111), Li7Ti5O12 (111) and α-Li2TiO3 (100), (110), and (111) surfaces using Hubbard-corrected density-functional theory (GGA+U), screening more than 600 stoichiometric Li4Ti5O12 and Li7Ti5O12 (111) surfaces. For Li4Ti5O12 and Li7Ti5O12 we find Li-terminated surfaces are more stable than mixed Li/Ti-terminated surfaces, which typically reconstruct. For α-Li2TiO3, the (100) surface energy is significantly lower than for the (110) and (111) surfaces, and is competitive with the pristine Li7Ti5O12 (111) surface. Using these stoichiometric surfaces as reference, we also model variation in Li surface coverage as a function of lithium chemical potential. For Li4Ti5O12, the stoichiometric surface is most stable across the full chemical potential range of thermodynamic stability, whereas for Li7Ti5O12, Li deficient surfaces are stabilised at low Li chemical potentials. The highest occupied electronic state for Li7Ti5O12 (111) is 2.56 eV below the vacuum energy. This is 0.3 eV smaller than the work function for metallic lithium, indicating an extreme thermodynamic drive for reduction. In contrast, the highest occupied state for the α-Li2TiO3 (100) surface is 4.71 eV below the vacuum level, indicating a substantially lower reduction drive. This result demonstrates how stoichiometry can strongly affect the thermodynamic drive for reduction at metal-oxide-electrode surfaces. In this context, we conclude by discussing the design of highly-reducible metal-oxide electrode coatings, with the potential for controlled solid-electrolyte-interphase formation via equilibrium chemistry, by electrode wetting in the absence of any applied bias.


Introduction
The global transition from fossil fuels to renewable low-carbon primary energy sources is, at present, hindered by the need for secondary energy storage technologies that can operate reliably and cheaply. Lithium-ion batteries are widely used for secondary energy storage in personal electronics, and increasingly in hybrid electric vehicles, but scaling commercial technologies up to grid-scale capacities presents a challenge. Conventional Li-ion batteries use graphite anodes, which are low cost and have excellent lithium-intercalation kinetics. The low intercalation potential of graphite with respect to Li/Li + means rapid charging causes metallic Li to plate at the electrodeelectrolyte interface. 1 Inhomogeneous Li plating can precipitate Li dendrite growth, eventually causing the cell to short-circuit. Conventional Li-ion batteries use liquid or polymer organic electrolytes, and the rapid release of energy during a short-circuit can initiate electrolyte combustion, presenting a serious safety concern. In addition, in graphite the intercalation and extraction of lithium produces large volume changes. Repeated charge-discharge cycles can cause the electrode to crack, potentially breaking contact between electrode particles and causing irreversible capacity loss. This manifests as a gradual degradation of battery performance and contributes to limited battery lifetimes, increasing the lifetime costs of grid-scale storage.
One strategy to address these problems is to replace graphite anodes with a material less prone to lithium plating or cracking. A promising alternative is Li 4 Ti 5 O 12 , which readily intercalates three lithium ions per formula unit at a voltage of 1.56 V versus Li/Li + to form Li 7 Ti 5 O 12 . 2 Li 4 Ti 5 O 12 offers high Li-insertion and extraction rates, and importantly shows excellent stability over repeated cycles, attributed to two properties. First, Li 4 Ti 5 O 12 is a "zero-strain" intercalation compound, with Li intercalation producing lattice parameter changes smaller than 0.1%. 3 Second, the relatively high potential for lithium intercalation of 1.56 V limits the formation of dendritic Li, which mitigates both the degradation of cell performance over repeated charge/discharge cycles and the risk of catastrophic short-circuiting.
The properties of bulk Li 4 Ti 5 O 12 have been studied in a number of previous works. [4][5][6][7][8] . 9 The operational characteristics of an electrode, however, depend not only on bulk properties, but also on the electrode-electrolyte interface. During Li + insertion and extraction, lithium ions move across this interface and through the electrode near-surface region. Local diffusion barriers, which may differ from bulk values, determine insertion and extraction kinetics and associated overpotentials. 10 Electrochemical side-reactions at the electrode surface, such as continuous reduction of the electrolyte to form a solid-electrolyte interphase (SEI), may also degrade cell performance over repeated cycles. The thermodynamic driving force for reductive surface reactions, involving electron transfer from the electrode to the electrolyte, depends on the binding energy for electrons at the surface (relative to a fixed reference, such as the vacuum energy). Surface electron binding energies may deviate from bulk values, due to band bending, and electrochemical reactivity and stability of electrode surfaces therefore depend on their composition and atomic geometry.
A rational development of improved energy storage solutions requires understanding the relationships between electrode surface composition, geometry, and resulting electrochemical properties (SEI formation and evolution included). The challenge of experimentally resolving atomicscale surface structure and electronic properties makes explicit computational modelling a pow-erful complementary approach for relating electrode surface chemistry to electrochemical performance. Here we focus on the case of Li 4 Ti 5 O 12 , which shows particularly interesting behaviour.
In 2012, Kitta et al. 11 studied the evolution of the atomic structure and electrochemical properties of a Li 4 Ti 5 O 12 (111) surface during initial lithium insertion and extraction cycles, using a combination of atomic force microscopy (AFM), transmission electron microscopy (TEM), and electron energy loss spectroscopy (EELS). Starting from a pristine atomically flat (111) surface, the first lithium insertion-extraction cycle produced an irreversible structural change, accompanied by a 10 nm increase in surface roughness. After this first cycle, the charge transfer resistance of the electrode/electrolyte interface fell by half, then remained constant for the following charge-discharge cycles. By analysing TEM data these authors identified an epitaxially-matched α-Li 2 TiO 3 surface-layer phase formed during the first insertion/extraction cycle.
An epitaxially matched surface-layer phase, such as α-Li 2 TiO 3 on Li 4 Ti 5 O 12 , may be considered as a solid-electrolyte interphase component. Because the electrochemical performance of an electrode depends on the surface composition, the observations of Kitta et al. suggest an intriguing strategy for tailoring electrode surface properties. Targetted in-situ growth of specific surface-layer phases may lead to enhanced electrode rate capabilities and stability, and correspondingly increased operational lifetimes. In this respect the Li 4 Ti 5 O 12 /Li 7 Ti 5 O 12 /α-Li 2 TiO 3 system represents an exemplar case for studying the role of surface composition on electrochemical characteristics, as well as being directly relevant to the use of Li 4 Ti 5 O 12 as a high-stability Li-electrode.
To understand how a surface-layer α-Li 2 TiO 3 phase affects the electrochemical properties of the Li 4 Ti 5 O 12 anode, there is a timely need for an atomically resolved structural description of the competing surfaces and a comparison of their electronic properties. These aspects are challenging to access experimentally: in the study of Kitta et al. the structural data lack the atomic resolution necessary to identify competing surface morphologies, while electronic properties, such as the electrostatic potential across the electrode-electrolyte interface region, are not accessible.
Density functional theory (DFT) is a useful tool in both these regards, because it provides a direct description of atomic scale geometries and of electronic structure, and for this reason DFT is a well established approach for studying simple surfaces. 12 In the case of Li  15 Only a single geometry was modelled for each surface, and it is not known, therefore, whether these surface energies represent thermodynamically favoured low energy surfaces, or whether more stable surfaces with different surface planes or alternate surface atom arrangements exist. The primary objective of this work is to provide an extensive energy screening of Li 4 Ti 5 O 12 , Li 7 Ti 5 O 12 , and α-Li 2 TiO 3 surfaces.
To this end, we report DFT calculations of the (111) Li 4 Ti 5 O 12 and Li 7 Ti 5 O 12 surfaces, and the (100), (110), and (111) surfaces of α-Li 2 TiO 3 , considering a total of more than 600 surface structures. For the Li x Ti 5 O 12 surfaces we consider competing surface terminations along the (111)oriented unit cell, and perform a search over different configurations and stoichiometries of undercoordinated cations at each exposed surface. For α-Li 2 TiO 3 the significant surface roughness observed by Kitta et al. 11 for the (111)-grown surface means other crystallagraphic surfaces might be present in the final as-grown surface morphology, and we therefore compare energies of three low-index surfaces.
A complete theoretical description of Li x Ti 5 O 12 surfaces under all accessible experimental conditions requires considering a comprehensive set of surface stoichiometries, each of which may become favoured at component atom chemical potentials. A computational study of all pos-sible surface stoichiometries is impractical: an infinite number of surface configurations may be constructed. To ensure our study is computationally tractable, we first restrict our attention to stoichiometric surface models. For the stoichiometric surface models with lowest energy we then consider adding or removing surface atoms, to understand how the surface structure varies with chemical conditions. We find that Li x Ti 5 O 12 (111) surfaces with pure lithium terminations are more stable than surfaces with mixed lithium-titanium terminations, which tend to reconstruct. For α-Li 2 TiO 3 the (100) surface energy is significantly lower than the (110) and (111) surface energies. This indicates that planar (111)-terminated surfaces are unstable with respect to highly-facetted (100)-  16 This is even smaller than the work function of metallic lithium of ∼ 2.9 eV, 17,18 which is experimentally observed to reduce electrolytes even in the absence of an applied bias. Zero-bias SEI formation has been observed in the lithium-ion cathodeLiMn 2 O 4 for surface facets with a large reduction drive, after electrolyte wetting. 19,20 The development of materials or coatings with highly reducing surface facets, which may allow controlled zero-bias SEI formation, is an interesting and possibly quite general design strategy for future high stability electrodes. For this strategy to be rationally explored, it is necessary to link the composition and structure of an electrode surface to the relevant redox chemistry thermodynamics, which we provide here for the competing phases and surface stoichiometries of lithium-titanate spinel anodes.

Methods
Calculations were performed using the DFT code VASP, 21,22 with valence electrons described within a plane-wave basis and an energy cutoff of 500 eV. Valence-core interactions were treated with the projector augmented wave (PAW) method, 23,24 with cores of [Mg] for Ti, [He] for O, and [He] for Li. Calculations were performed using the PBE generalised gradient approximation (GGA) functional, 25 supplemented with a Dudarev +U correction applied to the Ti d states (GGA+U). The previous study of Lu et al. presented EELS data for Li 7 Ti 5 O 12 that showed distinct "Ti 3+ " and "Ti 4+ " oxidation states, 7 alongside DFT calculations using both standard GGA (PBE), and GGA+U (PBE+U) functionals. These GGA calculations qualitatively failed to describe the distinct Ti oxidation states observed in the EELS spectra. This is due to the self-interaction error inherent to standard GGA (and LDA) functionals, [26][27][28] and similar behaviour is well known for many transition metal oxides with mixed formal oxidation states. [29][30][31] By applying a +U correction of U = 4.5 eV to the Ti d states, Lu et al. predicted charge disproportionation into distinct "Ti 3+ " and "Ti 4+ " oxidation states, recovering qualitative agreement with the experimental EELS data. We use this same value of U Ti d = 4.5 eV, noting this is close to the value of U Ti d = 4.2 eV used previously to study partially reduced TiO 2 . 32,32,33 To obtain equilibrium structures and reference energies for bulk Li 4  For all surface models, to minimise spurious slab-slab interactions a vacuum gap of at least 15 Å was placed between slab periodic images along the c direction normal to the surface plane. The reference energy for metallic lithium, used to calculate surface energies as a function of the lithium chemical potential, was calculated using a body-centered cubic 2-atom unit cell with a 16×16×16 Monkhorst-Pack k-point mesh.

α-Li 2 TiO 3 structure
Under ambient conditions, Li 2 TiO 3 preferentially adopts the monoclinic β phase, which has been broadly studied due to potential applications as a microwave dielectric and as a possible tritium breeder in future fusion reactors. [37][38][39] The α phase, which we are interested in here, is metastable in bulk systems. This phase can be considered a disordered pseudo-rocksalt, consisting of a fcc oxide-ion lattice with all the octahedral sites occupied by lithium or titanium. In this resepect, α-Li 2 TiO 3 is similar to Li 7 Ti 5 O 12 , but with the octahedral sites are occupied in a 2:1 Li:Ti ratio.  Figure 2). Hypothetical slabs with asymmetric layer sequences are therefore dipolar: their (111) surfaces are non-equivalent, leading to poorly defined surface energies. 41 The asymmetric charge distribution corresponds to a dipole perpendicular to the surface planes, which introduces long-ranged dipole-dipole interactions between periodic slab images, and surface energies formally diverge with increasing slab thicknesses. To avoid these issues we consider only symmetric layer stacking sequences, which give non-polar slabs with well defined surface energies.
In practice, this requires slabs with odd numbers of layers, and layers A or D at their centre. In the first instance, we consider surface models that maintain corresponding bulk stoichiometries, i.e. Li 4 Ti 5 O 12 or Li 7 Ti 5 O 12 . This means surface energies are simply given by the difference in energies between the two-dimensional slabs and equivalent bulk systems, according to where E slab is the energy of the surface cell, E bulk is the energy of an equal number of formula units in the bulk, and A is the surface area of one face in the slab model.
where ∆n Li is the number of lithium atoms added or removed at the surface, E Li is the lithium reference energy, calculated for metallic bcc Li, and µ Li is the lithium chemical potential. In a lithium-ion battery µ Li is equivalent to the cell voltage relative to metallic Li (scaled by Faraday's constant) in the limit that charging or discharging takes place reversibly.
Within the dual constraints of symmetric layer-stacking sequences and bulk stoichiometries,

Non-stoichiometric surfaces
Thus far we have considered only stoichiometric surface models. This restricts the possible surfaces to a number that is computationally tractable and simplifies the surface-energy analysis, because the calculated surface energies are independent of the component chemical potentials.
Lithium-ion batteries are dynamic systems, however, and it is important to consider the stabilities of competing surfaces under chemical conditions corresponding to cell operation. In particular, the lithium chemical potential, which is proportional to the cell voltage in the limit of reversible charging and discharging, may vary by several eV during cell cycling.
To investigate the effect of chemical conditions on surface stability, we took as starting templates the lowest energy stoichiometric surface models, and constructed a series of surface models with lithium added to or removed from the surface layer. As described above, for both Li 4 Ti 5 O 12 and Li 7 Ti 5 O 12 the stoichiometric (111) surfaces are more stable when Li-terminated than with mixed Li/Ti-termination, and we therefore only consider variable lithium-ion surface coverage.
We have not performed an exhaustive search of all possible surface configurations and stoichiometries. Instead we use the subset of surface sites occupied in the lowest energy stoichiometric configurations as templates for representative non-stoichiometric structures.
In the lowest energy Li 7 Ti 5 O 12 configuration, the surface-layer lithium is arranged in a hexagonal pattern (Figure 4)  This suggests that these observed ex-situ non-stoichiometric defective samples may be kinetically stabilised, and might not be representative of the same materials under charging / discharging conditions. For Li 7 Ti 5 O 12 the stoichiometric surface is favoured over nearly the whole region of thermodynamic stability. Within a narrow region of relatively low µ Li however, close to the stability limit with respect to Li 4 Ti 5 O 12 , partially lithium-deficient surfaces become favoured relative to the stoichiometric surfaces.

Electronic properties and thermodynamic reduction drive
The different structures and compositions of competing electrode surfaces correspond to different local potential profiles and electronic structures. These electronic differences are responsible for varied electrochemical behaviour with respect to lithium (de)intercalation, SEI formation, and overall electrode lifetimes. Surfaces with high electron chemical potentials-or equivalently, small workfunctions-should, if solvent relaxation effects are neglected, exhibit a more pronounced thermodynamic drive towards reduction of organic electrolytes, and might promote SEI formation even in the absence of an external applied voltage. 14,20 The atomistic details of such processes are at present far from clear. In particular it is unknown to what degree zero-bias (equilibrium formed) SEI's can perform better than SEI's formed during lithium-cycling i.e. via non-equilibrium chemistry. Computational modelling offers direct access to the electron chemical potential at different surfaces, and allows us to explore the scope of possible electronic behaviours. Furthermore, by identifying surfaces with noteworthy reduction potentials, we hope to stimulate experimental studies of zero-bias SEI formation in the context of possible improvements to lithium-ion-cell stabilities.
Having identified the low energy surface terminations for Li 4 Ti 5 O 12 (111) and Li 7 Ti 5 O 12 (111), and found the (100) surface preferred for α-Li 2 TiO 3 , we calculated vacuum-aligned energies for the highest occupied Kohn-Sham states for these three surfaces, to estimate the thermodynamic reduction drive in each case. These energies, E vac HOS were calculated for each slab as the difference between the electrostatic potential plateau for the vacuum and the energy of the highest occupied Kohn-Sham state, E HOKSS , 49 50 The vacuum potential and highest-occupied-state energies were calculated in each case using a geometry-optimised "double-thickness" surface slab: 13 layers for Li 4 Ti 5 O 12 and Li 7 Ti 5 O 12 (111) and 12 layers for α-Li 2 TiO 3 (100).
The calculated highest-occupied state energies, E vac HOS (Table 2)    In both structures, oxygen ions (red) form an fcc lattice, occupying the 32e sites, and the 16d octahedral sites (grey) are occupied by titanium and lithium at a ratio of 5 : 1. In (a) Li 4 Ti 5 O 12 , lithium also occupies the 8a tetrahedra (green). In (b) Li 7 Ti 5 O 12 , all cations are in octahedral sites, with the 16d octahedral sites (grey) occupied by titanium and lithium at a ratio of 5 : 1, and lithium in the 16c octahedra (green).  Blue and green polyhedra correspond to titanium and lithium occupied sites, respectively, and grey shows empty volume in the layer. Sites considered for the surface atoms are represented by dashed circles. White circles are surface tetrahedral sites, and black circles are surface octahedral sites. A-terminated surface models are constructed by partial occupation of the surface sites on the B sub-surface (a and b); D-terminated surface models are constructed by partial occupation of the surface sites on the C sub-surface (c and d).