Article pubs.acs.org/JPCC
(Sub)surface-Promoted Disproportionation and Absolute Band Alignment in High-Power LiMn2O4 Cathodes Ivan Scivetti* and Gilberto Teobaldi Stephenson Institute for Renewable Energy, Department of Chemistry, University of Liverpool, Liverpool L69 7ZF, United Kingdom S Supporting Information *
ABSTRACT: We present an isotropic (Ueff) and anisotropic (U−J) Hubbard and van der Waals (vdW)-corrected density functional theory study of bulk and low-index surfaces of lithium manganese oxide LiMn2O4 (LMO), a promising cathode material for high-power Li-ion batteries. Use of anisotropic (U−J) corrections in the simulation of bulk LMO leads to improved agreement with available experimental data, whereas vdW corrections do not affect the results. Carefully converged relaxation of slab geometries indicates that when vdW corrections are included the spinelreconstructed Li-terminated (111) surface is always energetically favored for both Ueff and (U−J) methods regardless of the LMO phase. In contrast, neglect of vdW corrections leads to the (001) surface in orthorhombic phase being favored when applying (U−J) corrections. Independent of the simulation protocol and crystalline phase, (111) truncation, reconstructed or not, promotes LMO disproportionation and appearance of Mn2+ cations without the need of any chemical or electrochemical surface treatment. Absolute band alignment of the considered surfaces reveals increased reductive propensity for the (111) terminations. Finally, our computational findings are discussed with respect to available data on the observed surface dependence of Mn disproportionation and electrochemical passivation of LMO substrates.
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Besides Mn dissolution into the electrolyte,13 several phenomena have been identified that affect LMO cathode performance: the occurrence of a first-order cubic-orthorhombic phase transition at room temperature (∼290 K) that can cause lattice stress and compromise the structural integrity of the cathode;14−20 formation of surface-dependent, differently effective, solid-electrolyte interphases (SEIs) from electrolyte decomposition;21−23 and creation of oxygen vacancies24,25 and Jahn−Teller distortions upon reduction of samples.10,14,26−28 In addition, LMO cathode performance has been observed to be strongly affected by surface morphology29−31 and termination32−37 as well as the presence of grain boundaries, surface impurities, and defects.21 Among the possible strategies to mitigate LMO degradation, the use of oxide coatings such as Al2O3 or MgO has been shown to significantly improve the stability and performance of LMO cathodes.38−40 Oxide coating restores the octahedral coordination of Mn atoms at LMO surfaces, inhibiting the formation of surface Mn3+ ions that are believed to disproportionate to Mn2+ (and Mn4+), eventually dissolving into the electrolyte. The established link between LMO surface morphology and composition on the one hand and electrochemical perform-
INTRODUCTION The transition from fossil fuels to typically dilute and intermittent renewable energy sources demands availability of efficient and industrially viable high-energy-density storage.1 To this end, improvement and further development of lithium-ion battery (LIB) technologies holds great potential and has been receiving growing academic and industrial interest.1−6 Costs and environmental concerns on the use of lithium cobalt oxide (LiCoO2) as standard cathode material in LIBs have led to extensive efforts being dedicated to the development of alternative cathode materials based on abundant, cheap, and environmental benign elements.7−9 In this context, spinel lithium manganese oxide LiMn2O4 (LMO) has emerged as a promising alternative cathode material, not only for its low cost, nontoxicity, and safety but also for its high operating potential and rate capability, all of which make LMO appealing for highpower electromotive applications.10,11 However, integration of LMO in commercial LIB cathodes has so far been hampered by the tendency of the material to degrade upon cycling, which leads to battery power fading and irreversible capacity loss. LMO degradation has been associated with the material tendency to disproportionation (2Mn3+ → Mn4+ + Mn2+) and dissolution of Mn2+ ions in the electrolyte.12 To overcome these limitations and to stabilize LMO to deliver its potential for high-power LIBs, growing research efforts have been directed to characterization and understanding of the evolution of the material and its interfaces upon cycling. © 2015 American Chemical Society
Received: July 7, 2015 Revised: August 25, 2015 Published: August 25, 2015 21358
DOI: 10.1021/acs.jpcc.5b06522 J. Phys. Chem. C 2015, 119, 21358−21368
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The Journal of Physical Chemistry C ances on the other,21,29−37 together with the lack of atomically and time-resolved insight into the mechanisms responsible of surface Mn3+ disproportionation and LMO degradation12,13 or extended cycling stability,31,37 make atomistic modeling of LMO surfaces and their interfaces highly valuable for the development of novel nanoengineered cathode solutions for LIBs. These considerations have prompted growing interest by the density functional theory (DFT) community in LMO and its interfaces. DFT studies and results have appeared for bulk LMO,41−45 vacuum-exposed LMO surfaces,44−46 and LMO doping47 and surface coating,48 as well as on Li mobility49 and organic solvent decomposition for variable Li content.22,23 In spite of the growing DFT research on LMO, the electronic structure and absolute bands alignment of LMO surfaces, which could be linked to the different reactivity and SEI formation of different LMO surfaces in the presence of the same electrolyte,21 have not been extensively considered in the literature so far. Given the experimental challenges in atomresolved characterization of local surface electronic band gaps (BGs) and lineups, these aspects deserve a dedicated and methodologically consistent computational study. Recent contrasting results on the electrochemical performances of cathodes prepared with octahedral, exposing mostly (111) facets, and truncated octahedral, exposing (111), (110), and (100) planes, LMO nanoparticles using the same binder and electrolyte31,37 add urgency to the definition of accurate and reliable atomistic models for LMO subsurface/surface/ electrolyte interfaces toward further fundamental understanding and optimization of LMO cathodes. Critically, the size of such interfaces and the occurrence of highly correlated 3d (Mn) electrons in LMO pose severe accuracy−viability compromises for DFT simulation. Although very promising results have appeared on the use of screened hybrid DFT for simulation of defective bulk LMO,42 simulations of several hundred atom models by this method are currently extremely demanding at the very least. The use of onsite Hubbard corrections, normally referred as DFT+U, offers a convenient numerical strategy to the deficiencies of standard semilocal DFT functionals in describing 3d-electroncontaining materials.50−54 Furthermore, the local nature of the correction is compatible with linear-scaling implementations of DFT, which makes it possible to simulate systems of a few thousand atoms on academically available hardware.55 Within the original formulation of DFT+U, or more precisely DFT+(U−J), both Coulomb and exchange local corrections are applied anisotropically to capture the angular dependence of the Hubbard subspace (d or f) projectors.50,51 A simplification of the original method can be obtained by spherically averaging the anisotropies of the Coulomb term, and ignoring the exchange contributions, leading to the “effective” isotropic DFT +Ueff approach. This is reported to be an usually acceptable approximation for light, early transition metal oxides.52−54 To the best of our knowledge, all the previous studies of LMO bulk and surfaces have been carried out using the isotropic DFT+Ueff approach. However, it has been recently found that the DFT +Ueff approach yields qualitatively wrong results for bulk rutile β-MnO2 and that explicit inclusion of anisotropies via the DFT +(U−J) method is preferred.56 Whether this conclusion holds also for β-MnO2 surfaces, or more relevant here, LMO bulk and surfaces has not been investigated yet, which motivates our interest. Further complications in the simulation of LMO interfaces with typical organic solvents for LIB electrolytes and SEI
formation stem from the need to account for dispersion interactions neglected by standard semilocal DFT functionals.57 Although the interplay between (isotropic or anisotropic) Hubbard and dispersion corrections could expectedly be critical for simulation of LMO−electrolyte interfaces, best practice for consistent simulation of bulk LMO as well as vacuum- and electrolyte-exposed LMO surfaces is, to the best of our knowledge, not available from the literature. This prompts careful investigation of the matter. Motivated by all these elements, here we present an extensive study of the role of LMO surface truncation and relaxation for Mn disproportionation and absolute bands alignment. Our study is complemented by careful investigation of the dependence of the computed results on the use of isotropic (DFT+Ueff) or anisotropic [DFT+(U−J)] Hubbard corrections in combination with inclusion and neglect of dispersion corrections.
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METHODS All the calculations in this work were spin-polarized and carried out using the DFT+U approach50−54 together with periodic boundary conditions (PBCs) and the projector-augmented wave method,58 as implemented in the VASP code.59−61 Following previous work,41 the electronic exchange-correlation was treated according to the GGA-PW91 approximation62 and the interpolation formula of Vosko et. al.63 We considered two different DFT+U alternatives: (i) the “fully anisotropic” approach where both Coulomb and exchange terms (U and J, respectively) are matrices that account for the spatial anisotropy of the d orbitals, and (ii) the effective U approach (Ueff), where U is spherically averaged and J is set to zero.52 In principle, the fully anisotropic scheme (U−J from now on) is a more accurate approximation for the description of the d orbitals and has been successfully applied to β-MnO2 to correct the limitations of the Ueff approach.56 However, the improvement in accuracy is governed by the accuracy of the U and J parameters. Following previous work,44,45,64 we set Ueff = 5.0 eV, and under the assumption that the Slater integrals F2 and F4 are weakly screened in crystals, we chose J = 1.2 eV, which corresponds to the computed value for Mn4+ in the atomic limit.65 Accordingly, in order to compare both DFT+U methods, the value of U for the (U−J) case was set to 6.2 eV. For easier comparison with previous results,42,45 we used cubic and tetragonal supercells containing eight formula units of LMO for bulk simulations. For the simulation of surfaces, we used the slabs approximation and tested the smallest thickness required to converge surface energies (see below). A vacuum separation of 10 Å was used to avoid spurious interactions between opposite surfaces of the PBC-replicated slabs. As discussed elsewhere,44−46 the low-index surfaces of LMO are polar and possess a net dipole moment. Because of the use of PBCs, such a dipole introduces undesirable artificial electrostatic interactions between the infinite replicas of the simulation cell, causing the energy of the system to diverge with the thickness of the slab. This severe drawback can be remedied by using either surface defects or reconstructions to cancel out the dipole moment.66,67 For simplicity and the sake of comparison with previous results,44−46 we applied the method of Tasker68 and only considered stoichiometric slabs, canceling the slab dipole moment by transferring atoms between the two opposite surfaces. This procedure and its application to LMO slabs has been thoroughly described previously.44,46 21359
DOI: 10.1021/acs.jpcc.5b06522 J. Phys. Chem. C 2015, 119, 21358−21368
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The Journal of Physical Chemistry C We used a plane-wave energy cutoff of 550 eV. For the Brillouin zone sampling of bulk calculations, we set 3 × 3 × 3 kpoints within the Monkhorst−Pack scheme,69 whereas for slabs calculations, we sampled the 2D Brillouin zone with 3 × 3 and 2 × 4 k-point grids for the (001) and the (111) surfaces, respectively. These parameters were checked to lead to values of total energy and magnetic moments converged within 5 meV and 0.02 μB, respectively. Given the far-from-immediate link between atom-partitioned (projected) charges and oxidation states for transition metal elements in oxides70,71 and following previous work,46 Mn4+, Mn3+, and Mn2+ sites were identified on the basis of the computed atomic magnetic moments whose magnitudes depend on the adopted DFT+U method as well as the crystalline phase and overall magnetic ordering. The range of computed magnetic moments of Mn4+ and Mn3+ in bulk are 3.03−3.40 and 3.88−4.00 μB, respectively. For surfaces, in contrast, we obtain 2.98−3.50, 3.77−4.03, and 4.55−4.60 μB for Mn4+, Mn3+, and Mn2+, respectively. The computed surfaceenhancement of Mn atomic moment is in line with the previous results in ref 46. We recall that computed magnetic moments for the Mn atoms as well as DFT+Ueff (U−J) total energy depend on both the value of Ueff(U−J) and the choice of the DFT+Ueff(U−J) projectors.72 Finally, for consistency with future simulations of LMO interfaces with the electrolyte, we also investigated the effects of including and neglecting dispersion interactions. To this purpose, we used the van der Waals (vdW)-corrected DFT formalism with the parametrization proposed by Grimme57 that accounts for vdW interactions via element-specific semiempirical pair potentials and a global scale factor (S6) that in turn depends on the adopted approximation to the exchangecorrelation potential. Here, we used the recommended S6 value of 0.7 for the PW91 exchange-correlation functional.57
Figure 1. Supercell model of bulk spinel LMO after structural optimization: Li (green), Mn3+ (blue), Mn4+ (purple), and O (orange). Orthogonal lattice vectors a, b, and c are set along , , and directions, respectively.
U correction for all Mn atoms, the same electronic occupancy and magnetic moment is computed for all Mn atoms. Hence, to enforce the presence of Mn atoms with different magnetic moments (oxidation states), it is necessary to break the symmetry, for which we propose the methodology explained in section S1 of the Supporting Information. In agreement with a recent computational study,42 we find that bulk total energy strongly depends on the distribution of Mn3+/Mn4+ in the crystal. The lowest-energy Mn3+/Mn4+ arrangement alternates pairs of Mn3+ and Mn4+ atoms along the [110] and [11̅0] directions as shown in Figure 1. This result applies to both the cubic and orthorhombic phases. For such a cation arrangement, the lowest-energy AFM ordering leads to a [↓↑↑↓] sequence of the magnetic moments for Mn atoms along the [110] direction and to a [↑↓↓↑] pattern along [11̅0] (or vice versa), in agreement with published results.41,45 Relative energies, Kohn−Sham (KS) BGs, structural parameters, and atomic magnetic moments for the lowestenergy AFM and ferro-magnetic (FM) orderings are summarized in Table 1, where we also compare the differences between the two DFT+U methods and available experimental values for the orthorhombic and cubic phases. Using these optimized lattice vectors, we also evaluate the effect of including vdW corrections (shown in parentheses). Regardless of the crystalline phase, the Ueff method consistently predicts FM ordering to be the lowest energy magnetic state. In contrast, AFM ordering is energetically favored by the U−J method, which also predicts a slightly contracted volume for the optimized supercell, in qualitative agreement with the computational analysis for (unlithiated) βMnO2.56 Computed lattice parameters with the Ueff method are in good agreement with previous work,45 although we obtain a slightly stretched value of c (∼7%) for the orthorhombic phase (in the adopted tetragonal supercell) with respect to the experiments. We refer the interested reader to section S-3 of the Supporting Information for further discussion of this aspect. The computed average Mn−O distances are larger for Mn3+ than for Mn4+, indicative of local Jahn−Teller distortions for both crystalline phases, as previously reported.19,20,41,42 In addition, we find that the computed average Mn−O distances depend very little on the modeled FM or AFM magnetic ordering. With deviations smaller than 0.03 μB, the calculated atomic magnetic moments turn out to be independent of the crystalline phase. Negligible dependence on the overall AFM or FM ordering is also found for the magnetic moment of Mn3+. Conversely, FM ordering is computed to slightly increase
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RESULTS AND DISCUSSION A recent DFT study of (unlithiated) bulk β-MnO2 has demonstrated that different energetically favored magnetic orderings and BGs can be obtained depending on the use of isotropic Ueff or anisotropic U−J corrections for the Mn atoms.56 Whether this finding also holds for lithiated LiMn2O4 bulk and surfaces has, to the best of our knowledge, not yet been considered, which motivates the following sections. Bulk LMO. LMO crystallizes in a spinel-type structure, with Mn atoms in an oxidation state of either +3 or +4 and overall anti-ferro-magnetic (AFM) ordering. Above 300 K, the crystal is found to be cubic (space group Fd3̅m) with Mn3+ and Mn4+ cations occupying randomly distributed sites. As the temperature is decreased below ∼290 K, the structure undergoes a phase transition to an orthorhombic phase with a well-defined charge ordering for the Mn3+/Mn4+ cations.19,20,73 Below 100 K, a second structural transition is observed, with coexistence of orthorhombic and tetragonal phases down to 40 K, below which the tetragonal phase is preferred.74 Figure 1 shows the bulk spinel structure with eight LiMn2O4 formula units. Contrary to the primitive cell, which contains only two formula units, the adopted model makes it possible to explore configurations with longer-range charge and spin orderings, which have been found to be important for the computation of LMO energy.41,42,45 However, simulation of bulk LMO with Mn atoms in different oxidation states is not trivial. In fact, when setting the initial atomic positions on the basis of the spinel space group symmetry and applying the same 21360
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Table 1. Computed Energy Differences with Respect to FM Ordering (ΔE), Kohn−Sham Band Gaps, Optimized Lattice Vectors, Selected Interatomic Distances, and Atomic Magnetic Moments (μ) of Bulk LMO in the Orthorhombic and Cubic Phases for the DFT+Ueff and DFT+(U−J) Methods (PW91 Functional)a Ueff = 5.0, J = 0 eV magnetic order ΔE (meV) band gap (eV) a (Å) b (Å) c (Å) O−Mn3+ (Å) O−Mn4+ (Å) μ Mn3+ (μB) μ Mn4+ (μB)
AFM +107 (+106) 0.77 (0.78) 8.27 8.27 8.78 2.06 (2.06) 1.95 (1.95) 3.98 (3.98) 3.30 (3.30)
FM 0 0.38 8.28 8.28 8.79 2.06 1.96 3.99 3.38
magnetic order ΔE (meV) band gap (eV) a (Å) O−Mn3+ (Å) O−Mn4+ (Å) μ Mn3+ (μB) μ Mn4+ (μB)
AFM +139 (+119) 0.69 (0.75) 8.43 2.06 (2.06) 1.95 (1.95) 3.99 (3.99) 3.31 (3.31)
FM 0 0.29 8.44 2.06 1.96 4.00 3.40
U = 6.2, J = 1.2 eV Orthorhombic Phase AFM −47 (−47) (0.40) 1.20 (1.21) 8.22 8.22 8.80 (2.06) 2.06 (2.06) (1.95) 1.94 (1.94) (3.99) 3.88 (3.88) (3.38) 3.03 (3.02) Cubic Phase AFM −41 (−58) (0.30) 1.09 (1.11) 8.40 (2.06) 2.05 (2.05) (1.95) 1.94 (1.94) (4.00) 3.89 (3.89) (3.40) 3.03 (3.02)
FM 0 0.83 8.23 8.23 8.80 2.06 1.94 3.89 3.10 FM 0 0.71 8.41 2.05 1.94 3.91 3.11
experiment AFM (0.85)
(2.06) (1.94) (3.89) (3.10)
8.25b 8.29b 8.20 2.01−2.02c 1.91−1.97c 3.619 AFM
(0.72) (2.05) (1.94) (3.90) (3.11)
1.43,75 1.876 8.25 2.07 1.91
a Results for vdW-corrected simulations are reported within brackets. Experimental structural data is from Ishizawa et al.20 bValues are 1/3 of the lattice length of the experimental superstructure (Supporting Information). cReported occurrence of different coordination geometries for Mn atoms of the same oxidation state.
(by ∼0.1 μB) the magnetic moment for Mn4+. Finally, comparison between Ueff and U−J results indicate that the U−J approach leads to a reduction of the computed magnetic moments. Such a reduction depends on the Mn oxidation state: 0.1 and 0.3 μB for Mn3+ and Mn4+, respectively. Independent of the DFT+U approach, modeled magnetic ordering, and crystalline phase, a nonzero BG is consistently computed for bulk LMO, and its value ranges from 0.29 eV (FM cubic phase at Ueff level) to 1.20 eV (AFM orthorhombic phase at U−J level). BGs using the U−J method are systematically larger (by ∼0.4 eV) than those computed with the Ueff approach. Moreover, the computed BGs for AFM ordering are also ∼0.4 eV larger than those for FM states, regardless of the use of the Ueff or U−J method. (See Figures S2 and S3 for the computed partial density of states (PDOS) in orthorhombic and cubic phases, respectively.) These findings are in qualitative agreement with the trends computed for (unlithiated) rutile β-MnO2.56 It thus transpires that relative energies and computed BGs also non-negligibly depend on the use of isotropic (Ueff) or anisotropic (U−J) Hubbard corrections for bulk LiMn2O4. Finally, in view of the possibly important role of vdW interactions for the adsorption of organic electrolyte solvents on LiMn2O4 surfaces, we investigated also the dependence of LMO bulk results on the use of vdW corrections. As shown in Table 1, vdW corrections (in the Grimme D2 parametrization)57 are found to negligibly affect the DFT+Ueff and DFT +(U−J) relative energies, magnetic ordering, and optimized geometries for bulk LiMn2O4. In the following section, we explore whether the same holds also for LiMn2O4 surfaces. Vacuum-Exposed Surfaces. Exposed LMO surfaces are experimentally known to strongly affect the electrochemical performances and stability of LMO cathodes.21,31,37 Different LMO surfaces have been found to react differently when
contacted with the same organic electrolyte (1 M LiPF6 in a solution of ethylene carbonate/diethyl carbonate with 3:7 molar ratio), leading to different surface reconstructions and differently effective SEI.21 The established link between the initial surface atomic structure, SEI formation, and emerging properties and stability of LMO cathodes makes accurate simulation and insight into LMO surfaces necessary for future investigation of electrolyte decomposition and SEI formation at LMO cathodes. Vacuum-exposed LMO surfaces have been the subject of previous DFT studies, which have focused mainly on the relative energies of different surface terminations,44−46 LMO dissolution in contact with water77 and organic solvents.22,23 However, to the best of our knowledge, the electronic structure and absolute bands alignment of LMO surfaces, which could be linked to the observed different reactivity and SEI formation of different LMO surfaces in the presence of the same electrolyte,21 have not been previously discussed. Furthermore, the established importance of anisotropic (U−J) Hubbard corrections for manganese oxide systems56 and the use of exclusively the isotropic (Ueff) method in previous DFT investigations of LMO22,23,44−46 prompts for careful consideration of the role of isotropic and anisotropic Hubbard corrections for vacuum-exposed LMO surfaces. Results on LMO lowest-energy surfaces have led to some controversy. Ex situ experimental characterization of LMO surfaces shows the (111) truncation to be predominant in LMO nanocrystals, independent of their morphology.33,34,36 Conversely, Hubbard-corrected DFT (DFT+U) molecular dynamics (MD) simulations suggest that the (001)-Literminated surface is energetically favored.46 This controversy has been recently reconciled by DFT+Ueff findings that the antisite spinel reconstruction (swapping surface Mn and subsurface Li atoms) makes the reconstructed (111)-Li21361
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These results demonstrate that the approximation of fixing the inner atomic layers can be problematic for LMO when the number layers is not sufficiently large. Accordingly, all surface calculations were conducted by allowing full relaxation of all the atoms in the slab. For further technical details, we refer the interested reader to section S-2 of the Supporting Information. The (001)-Li-terminated surface (referred to as (001)-Li from now on) was modeled with overall FM and AFM ordering using 16- and 24-layer slabs.79 For this surface, Tasker’s condition is fulfilled by transferring only one Li atom to the opposite surface of the slab. The lowest energy configuration is obtained for the Mn3+ and Mn4+ arrangement shown in Figure 3 (left panel). The outer undercoordinated Mn atoms are all found to be Mn3+. Cation ordering is preserved as the slab thickness is increased from 12 to 24 layers, and the slabs are computed to maintain the bulk Mn3+/Mn4+ (1:1) ratio. The central part of the 24-layer slab is computed to keep the bulk Mn cation ordering (Figure S4, left panel), which indicates the existence of a bulk region inside the slab and justifies the use of the surface energy according to eq 1. Computed surface energies for FM and AFM orderings (Table 2) show that at least for 24 layers FM ordering is always energetically favored regardless of the adopted DFT+U method, the crystalline phase, and the inclusion or neglect of vdW corrections. Because the U−J method favors AFM for the bulk (Table 1) but FM ordering for the (001)-Li surface (Table 2), it is worth reporting that in our tests the relative energy between FM and AFM solutions going from 16- to 24-layer slabs was found to decrease from 87 to 34 meV for the orthorhombic phase and from 132 to 116 meV for the cubic phase. Thus, in spite of the obvious converge of the surface energy (Figure 2), slabs thicker than 24 layers may lead to energetically favored AFM ordering, especially for the orthorhombic phase. Given the substantial computational cost in simulating ≥32-layer slabs (>224 atoms), we did not investigate further into this aspect. The situation is different for the (111) surfaces where, besides the occurrence of Mn3+ and Mn4+, we also compute the presence of Mn2+, in agreement with previous work.46 For the (111)-MnLi surface (Figure 3, central panel), Tasker’s condition is fulfilled by transferring one Mn and two Li atoms to the opposite surface. The appearance of Mn2+ cations (one at each exposed surface) is the result of their location and undercoordination (from sixfold to threefold), which limits their hybridization with oxygen atoms. As a result, the total number of Mn3+ cations in the slab decreases by four, whereas the Mn4+ cations increase by two, consistent with the known tendency of LMO to disproportionation12 and earlier Ueff results for this unreconstructed surface.46 Notably, Mn2+ cations keep their oxidation state when swapped with the Li atoms of the next available layers to form the spinel-reconstructed (111)-Li surface (Figure 3, right panel). Because the reconstructed (111)-Li surface was not sampled in the MD study of Benedeck et al.46 and the surface Mn oxidation state was not analyzed in the work of Karim et al.,45 this is, to the best of our knowledge, the first time that occurrence of subsurface Mn2+ is documented. These results indicate that both surface (threefold) and subsurface (fourfold) undercoordination of Mn atoms are active in promoting Mn disproportionation. That is, initial appearance of (sub)surface Mn2+ ions in vacuum-exposed LMO surfaces is a ground-state property of (111)-terminated but not (001) surfaces that does not require any chemical or
terminated surface energetically favored, in line with experiments.44,45 Accordingly, in the following we only consider the reported lowest energy LMO surfaces, namely, the (001)-Literminated, the (111)-MnLi-terminated, and the spinelreconstructed (111)-Li-terminated terminations.44−46 Surface and Slab Energies. To compare the energetics between different surfaces, it is customary to use the surface energy, γ, defined as γ=
Eslab − N ϵbulk 2A
(1)
where Eslab is the total energy for the slab, N is the total number of atoms, ϵbulk is the bulk energy per atom, and A is the surface area of the slab. The factor 2 is due to the presence of two surfaces in the modeled slab. The main advantage in using this quantity resides in the possibility of comparing the surface energies for slabs with different number of atoms, without the need of more elaborate grand canonical formalisms.78 Conceptually, the slab model for the simulation of surfaces is an approximation that increasingly improves with the number of atomic layers. It is thus essential to determine how many atomic layers in the slab are necessary to obtain converged surface energies while keeping the system size tractable for computation. The customary procedure is to relax the outer layers of the slab while fixing the inner layers to the bulk geometry. This approximation rests on the assumption that termination and surface effects are screened by the atomic and electronic relaxation of the outer layers with negligible effects over the electronic and atomic structure at the inner layers of the slab. To investigate the convergence of the computed LMO surface energies with respect to the slab thickness, (cubicphase) (001)-Li-terminated surface was simulated using the Ueff method for slabs of 8, 16, and 24 layers with AFM ordering. Here, we assumed that the energetically favored bulk AFM ordering (Table 1, Ueff results) is preserved for LMO surfaces. This assumption is explicitly tested in the following. Figure 2 shows that the computed surface energy decreases as the number of layers that are allowed to relax during the simulation (free atomic layers) is increased. When all layers are allowed to relax, we compute the same surface energy for the 8-, 16-, and 24-layer slabs. Thus, complete relaxation of 8- and 16-layer slabs turns out to be necessary for evaluation of wellconverged surface energies for the (001)-Li-terminated surface.
Figure 2. Convergence of the surface energy of the (001)-Literminated slabs as a function of the number of (outermost) atomic layers allowed to relax. The horizontal dotted line (surface energy for the fully relaxed 24-layer slab) is a guide to the eye. 21362
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Figure 3. Side and top views of the considered LMO slabs. Only the two outermost atomic layers are displayed in the top views. The in-plane periodicity is marked by the black box. Light-blue and pink backgrounds show that the arrangement for the Mn cations is preserved when increasing the slab thickness. Mn3+ (blue), Mn4+ (purple), Mn2+ (yellow), O (orange) and Li (green).
Table 2. Computed Surface Energies (J/m2) for the (001)-Li Surface of the Orthorhombic and Cubic Phase of LMO in AFM and FM Ordering for the Ueff and the (U−J) Methods with (PW91-vdW) and without (PW91) vdW Corrections Ueff = 5.0, J = 0 eV cubic PW91 PW91-vdW
U = 6.2, J = 1.2 eV ortho
cubic
ortho
AFM
FM
AFM
FM
AFM
FM
AFM
FM
0.65 0.88
0.62 0.85
0.74 0.95
0.71 0.92
0.62 0.85
0.59 0.83
0.72 0.94
0.70 0.92
Figure 4. Computed relative energies (eV) for the considered surfaces of orthorhombic (Ortho.) and cubic LMO at Ueff and U−J levels with (vdW, right panel) and without (PW91, left panel) dispersion corrections for overall FM ordering.
energies as defined in eq 1 is not fully appropriate in this case because the slab lacks a bulklike region. Accordingly, it is now mandatory to compare slab energies for systems with the same stoichiometry and overall number of atoms. For LMO, the minimum number of atomic layers that comply with this requirement is 24, which represents a total of 168 atoms for the stoichiometric slab models. As shown in Figure 4 (left panel), without vdW correction the (111)-Li surface is always energetically favored, unless the phase is orthorhombic and the U−J method is used in which case the (001)-Li surface turns out to have the lowest energy. These results highlight at least three important aspects: First, neglecting kinetics considerations, cooling of LMO samples (for instance, during inactivity of the cathode) and activation of cubic → orthorhombic transition may lead to surface reconstruction and ensuing stress or modification of the SEI, which in turn may affect the SEI aging and calendar life of the cathode. Second, the use of isotropic (Ueff) or anisotropic (U−
electrochemical treatment. These results are in contrast with the widespread model, based on interpretation of surfaceinsensitive powder X-ray diffraction data,12 of occurrence of Mn2+ exclusively at LMO surfaces (i.e., no Mn2+ in the subsurface region). These findings also suggest that oxide coating of reconstructed (111)-Li surfaces, leaving the subsurface Mn2+ undercoordinated, may not be very effective in suppressing Mn disproportionation. The present simulations, nevertheless, do not allow us to conclude on the atomistic mechanism of Mn2+ dissolution in the electrolyte. Work along this line is in progress and will be reported elsewhere. Similar to the (001)-Li surface, the ordering for Mn cations in both (111) surfaces is preserved when increasing the number of atomic layers from 16 to 24. Nevertheless, we note that the central part of the slab does not keep the bulk cation ordering (Figure S4, right panel). This result originates from the appearance of Mn2+ cations and ensuing change of the overall Mn3+/Mn4+ (1:1) ratio in the system. Thus, the use of surface 21363
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Figure 5. Computed spin-resolved DOS (filled gray), and O (red) and Mn (blue) projected PDOS for the considered surfaces of cubic LMO at Ueff and U−J levels with inclusion of vdW corrections (FM ordering). Spin-up (-down) PDOS are reported as positive (negative) values.
J) Hubbard correction is clearly shown to non-negligibly affect the relative energy of LMO surfaces, opening up potential controversy when comparing results obtained with the two approaches. Third, in spite of the expectedly ionic nature of LMO, use or neglect of vdW corrections can lead to substantially different relative energies between LMO surfaces, as shown in Figure 4 for (001)-Li and (111)-Li, potentially causing further controversy when comparing results for vacuum- and electrolyte-exposed LMO surfaces obtained with different treatments of dispersion interactions. The present results for the cubic phase agree qualitatively with the results of Karim et al.,45 obtained under the assumption of AFM ordering with the Ueff method. Conversely, Benedeck et al.46 concluded that the (001)-Li surface was the lowest energy surface on the basis of a MD DFT+Ueff study for FM ordering. The MD simulations did not show evidence of the inverse spinel-reconstructed (111)-Li surface (at least at 300 K within the sampled 1 ps). However, using the simulation parameters of this MD study,46 we found that the (001)-Li and (111)-MnLi surfaces are 1.15 and 3.41 eV higher in energy than the (111)-Li surface,80 respectively. These results indicate that if the reconstructed (111)-Li surface had been sampled during the MD trajectory then it would have resulted in the lowest surface energy. When including vdW corrections, the (111)-Li surface is consistently found to be energetically favored, regardless of the crystalline phase and DFT+U method (Figure 4, right panel). This demonstrates that in contrast to the bulk case inclusion of vdW corrections which is expected to improve the description of organic adsorbates on LMO surface can be decisive also for the relative energy of the pristine vacuum-exposed LMO surfaces. Surface Electronic Structure. Although the considered LMO surfaces have been previously studied,44−46 to the best of our knowledge, their electronic structure has never been reported. To investigate the electronic structure of the considered LMO surfaces, we computed total density of states (DOS) and Oand Mn-resolved PDOS. Here, we report only the results for
the 24-layer slabs of the cubic phase modeled with inclusion of vdW corrections. Results for the energetically favored FM ordering using the Ueff and U−J methods are presented in Figure 5. Independent of the DFT+U method, both (001)-Li and (111)-MnLi surfaces preserve an electronic BG (Figure S3), with minimal changes from the bulk value. In contrast, the results for the (111)-Li surface depend qualitatively on the DFT+U approximation: Although metalization is computed at Ueff level, the U−J approach predicts the surface to be semiconducting, even though the BG is reduced by half of its bulk value. Once again, the use of isotropic Ueff or anisotropic U−J Hubbard corrections is found to majorly affect the simulated results, potentially causing misleading conclusions on the metallicity of LMO surfaces. Regardless of the adopted Ueff or U−J method, PDOS analysis reveals strong hybridization between O and Mn atoms resulting in contributions from both O and Mn atoms to the KS states around the Fermi level. Overall, the simulations indicate larger O contributions to the high-energy occupied KS states and nearly equal O and Mn projection of the low-energy empty KS states. With noticeably larger contributions from O states to both occupied and empty KS states, the only exception to this trend are the Ueff results for the (111)-Li surface. For the specialist reader, we report that neglect of vdW corrections was tested to minimally change the computed (P)DOS results for LMO surfaces from those displayed in Figure 5. We also analyzed the (P)DOS of the considered surfaces for orthorhombic LMO (Figure S5) and found no negligible change apart from the opening of a small (∼0.1 eV) BG for the (111)-Li surface at Ueff level. Analysis of the low-energy conduction band (CB) edge for the considered surfaces at U−J level reveals interesting features. In all cases, the states participating to the CB edge turn out to be localized in the bulk region of the slabs (Figure S6). However, the CB edge is computed to span different Mn cations depending on the given surface. For the (001)-Li surface, the CB edge is evenly distributed between Mn3+ and 21364
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The Journal of Physical Chemistry C Mn4+ cations. Conversely, the CB edge of the (111) surfaces is computed to be distributed mainly on Mn4+ sites (Figure S6). These results suggest that neglecting structural relaxation and bias effects the conductance of extra electrons in energy-favored (111) LMO substrates should take place mainly in the subsurface region and involve Mn4+ sites. In turn, this should non-negligibly affect the reductive chemistry of electron-rich LMO substrates during the initial stages of cathode charging (battery discharge), expectedly leading to a hindered kinetics for possible reduction of the electrolyte on the energy-favored LMO (111) surfaces. Slab Vacuum-Aligned Valence Band Edges. Different surfaces of LMO have been observed to react differently when placed in contact with the same electrolyte, with wetting of the (111) but not of the (110) surface leading to pristine SEI formation.21 The evidenced surface-dependence of LMO surface reactivity toward the same organic solvent prompts investigation of the absolute band alignment of LMO surfaces, which could be related to (if not responsible for) the different reactivity toward the same electrolyte. To this end, we investigated the position of the slab valence band (VB) edge (Fermi energy) with respect to the vacuum energy. Given the use of the (same) vacuum level as reference, higher-energy VB edges corresponding to higher-energy Fermi levels corresponding to smaller work function values are indicative of possible larger reduction propensity. This analysis neglects any reduction kinetics consideration as well as the role of electrolyte structuring at the electrode and ensuing modifications of the interface local potential.81−83 Figure 6 shows the vacuum-aligned VB edges for the considered surfaces as a function of the adopted DFT+U
the neglect vdW corrections, but because of changes in the relaxed slab geometries, values were found to increase by ∼0.2 eV. It is interesting to note that the LMO(111) surfaces observed to decompose organic electrolyte and lead to SEI formation in the absence of any applied bias21 turn out to have the highestenergy VB edges and hence an expected larger reduction drive. This may explain the observed increased reactivity of (111) terminations toward the electrolyte with respect to other crystallographic cuts.21 These hypotheses will be further tested by explicit simulation of LMO wetting by organic electrolyte (in progress).
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CONCLUSIONS Extensive isotropic (Ueff) and anisotropic (U−J) Hubbard- and vdW-corrected DFT simulation of bulk, surface-induced disproportionation and absolute band alignment for orthorhombic and cubic-phase LMO indicates the following: (i) The total energy of bulk LMO is dominated by the Mn3+ and Mn4+ ordering in the crystal with secondary effects due to FM or AFM ordering. Regardless of the cubic or orthorhombic phase and the use of the Ueff or (U−J) method, bulk LMO is computed to be a semiconductor (as in the experiment) with a BG in the 0.4−1.2 eV range. (ii) Use of the U−J method for bulk LMO favors AFM ordering and leads to wider BGs. Conversely, the Ueff approach favors FM ordering and results in narrower BGs. Inclusion of vdW corrections does not alter these conclusions. (iii) With the only exception of orthorhombic LMO at (U−J) level without inclusion of vdW corrections, favoring the (001)-Li surface, the spinel-reconstructed (111)-Li surface is found to be always energetically favored. Inclusion of vdW corrections in the simulations leads to the spinel-reconstructed (111)-Li surface being energetically favored regardless of the LMO crystal phase and DFT+U method. For the considered slab thickness (up to 24 layers and 168 atoms), FM ordering is always energetically favored. (iv) Both MnLi-terminated ((111)-MnLi) and reconstructed Literminated ((111)-Li) surfaces are found to contain surface and subsurface Mn2+ cations as a result of Mn undercoordination. By altering the bulk Mn3+/Mn4+ (1:1) ratio, (111)-promoted surface and subsurface disproportionation is consistently computed to affect the Mn3+/Mn4+ ordering in the whole slab, preventing the appearance of bulklike regions. (v) The Literminated (001) surface maintains the bulk Mn3+/Mn4+ (1:1) ratio, with no appearance of surface or subsurface Mn2+ cations. (vi) Regardless of the DFT+U method and inclusion or neglect of vdW corrections, the (111) and (100) surfaces of orthorhombic LMO are modeled to be semiconducting with BGs in the 0.1−0.7 eV range. (111) and (100) cubic LMO surfaces at U−J level are also found to be semiconducting with BGs in the 0.2−0.7 eV range. Conversely, metalization is computed for the reconstructed (111)-Li-terminated surface of cubic LMO when using the Ueff method. Experimental electronic characterization of single-crystal LMO surfaces, to the best of our knowledge not available in the literature, would be highly desirable to directly validate these results. (vii) Vacuum-aligned VB edges are found to be practically independent of the DFT+U method and the orthorhombic or cubic phase. The VB edges are modeled to increase in energy from (001)-Li (−5.6 eV) to spinel-reconstructed (111)-Literminated (−5.1 eV) and to (111)-MnLi (−4.2 eV). On the basis of these results and in view of the need of accounting for dispersion interactions in the simulations of
Figure 6. Vacuum-aligned VB edge for the considered surfaces of orthorhombic (Ortho.) and cubic LMO in FM ordering at Ueff and U− J levels with inclusion of vdW corrections.
method including vdW corrections. The adopted slab thickness (24 layers) was tested to yield results converged to within ±0.01 eV. The (001)-Li VB edge is the lowest (−5.6 eV), whereas the (111)-MnLi surface exhibits the highest VB edge (−4.2 eV). Spinel reconstruction of the (111) face, leading to the (111)-Li surface, is found to lower the VB edge by 1.0 eV. Thus, as a result of the different cation distribution and surface relaxation, the VB edge of different LMO surfaces can change as much as 1.5 eV, with potential differences in their (opencircuit, zero bias) reactivity toward the electrolyte. As shown in Figure 6, the computed values for the VB edges are found to be practically independent of the DFT+U method and the crystalline phase. Finally, we observed that the computed trend for VB edges is qualitatively unaffected by 21365
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LMO interfaces with organic electrolyte, use of anisotropic (U−J) Hubbard and vdW corrections for the simulation of LMO surfaces appears to be advisable in order to avoid contradictory results.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b06522. Methodology to compute bulk LMO; methodology to compute LMO surfaces; experimental versus computed results for bulk LMO; (P)DOS for LMO in orthorhombic and cubic phase; cation ordering for bulk LMO; (P)DOS of orthorhombic LMO surfaces; low-energy conduction band edge of LMO surfaces. (PDF)
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AUTHOR INFORMATION
Corresponding Author
*Phone: +44 151 795 8132. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Support from the EU FP7 program SIRBATT (contract no. 608502) is gratefully acknowledged. G.T. is supported by EPSRC UK (EP/I004483/1). This work made use of the HPC Wales, N8 (EPSRC UK EP/K000225/1), and ARCHER (via the UKCP Consortium, EPSRC UK EP/K013610/1) HighPerformance Computing facilities. We are grateful to Kevin Leung, Oleg Borodin, Khang Hoang, Altaf Karim, Emiliano Poli, Joshua Elliott, Stefano Passerini, and Nina Laszczynski for useful discussions. We have created a new data catalogue deposit, available with the DOI http://dx.doi.org/10.17638/ datacat.liverpool.ac.uk/54.
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DOI: 10.1021/acs.jpcc.5b06522 J. Phys. Chem. C 2015, 119, 21358−21368
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The Journal of Physical Chemistry C (75) Raja, M.; Mahanty, S.; Ghosh, P.; Basu, R.; Maiti, H. AlanineAssisted Low-Temperature Combustion Synthesis of Nanocrystalline LiMn2O4 for Lithium-Ion Batteries. Mater. Res. Bull. 2007, 42, 1499− 1506. (76) Kushida, K.; Kuriyama, K. Observation of the Crystal-Field Splitting Related to the Mn-3d Bands in Spinel-LiMn2O4 Films by Optical Absorption. Appl. Phys. Lett. 2000, 77, 4154−4156. (77) Benedek, R.; Thackeray, M. M.; Low, J.; Bucko, T. Simulation of Aqueous Dissolution of Lithium Manganate Spinel from First Principles. J. Phys. Chem. C 2012, 116, 4050−4059. (78) van de Walle, C. G.; Neugebauer, J. First-Principles Calculations for Defects and Impurities: Applications to III-nitrides. J. Appl. Phys. 2004, 95, 3851−3879. (79) The choice of the number of layers is not arbitrary but rather follows the bulk layer stacking along < 001> while keeping the stoichiometric of the formula unit the same.44,46 The same applies to the (111) surface, for which muliples of 12 layers have to be considered. (80) Computed values from ref 46 are 0.58 and 0.85 J/m2 for the (001)-Li and (111)-MnLi surfaces, respectively. (81) Nielsen, M.; Björketun, M. E.; Hansen, M. H.; Rossmeisl, J. Towards First Principles Modeling of Electrochemical Electrodeelectrolyte Interfaces. Surf. Sci. 2015, 631, 2−7. (82) Hormann, N. G.; Jackle, M.; Gossenberger, F.; Roman, T.; Forster-Tonigold, K.; Naderian, M.; Sakong, S.; Gross, A. Some Challenges in the First-Principles Modeling of Structures and Processes in Electrochemical Energy Storage and Transfer. J. Power Sources 2015, 275, 531−538. (83) Leung, K.; Leenheer, A. How Voltage Drops Are Manifested by Lithium Ion Configurations at Interfaces and in Thin Films on Battery Electrodes. J. Phys. Chem. C 2015, 119, 10234−10246.
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NOTE ADDED AFTER ASAP PUBLICATION This paper was published on September 2, 2015. The Acknowledgments section has been updated. The revised version was re-posted on September 8, 2015.
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DOI: 10.1021/acs.jpcc.5b06522 J. Phys. Chem. C 2015, 119, 21358−21368
