Mapping Structural Changes in Electrode Materials: Application of the

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Chemistry of Materials

Mapping Structural Changes in Electrode Materials: Application of the Hybrid Eigenvector-Following DFT Method to Layered Li0.5MnO2 Ieuan D. Seymour,† Sudip Chakraborty,‡ Derek S. Middlemiss,§ David J. Wales† and Clare P. Grey† * †

Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK.

‡

Department of Physics and Astronomy, Uppsala University, Uppsala, SE 75120, Sweden.

§

Department of Chemistry, University of Warwick, Coventry, CV4 7AL, UK.

ABSTRACT: The migration mechanism associated with the initial layered-to-spinel transformation of partially delithiated layered LiMnO2 was studied using hybrid eigenvector-following coupled with density functional theory. The initial part of the transformation mechanism of Li0.5MnO2 involves the migration of Li into both octahedral and tetrahedral local minima within the layered structure. The next stage of the transformation process involves the migration of Mn and was found to occur through several local minima, including an intermediate square pyramidal MnO5 configuration and an independent Mn3+ to Mn2+ charge transfer process. The migration pathways were found to be significantly affected by the size of the supercell used and the inclusion of a Hubbard U parameter in the DFT functional. The transition state searching methodology described should be useful for studying the structural rearrangements that can occur in electrode materials during battery cycling, and more generally, ionic and electronic transport phenomena in a wide range of energy materials.

Introduction Significant efforts have been dedicated to finding cheaper and less toxic Li ion cathode materials to replace the widely used LiCoO2. One class of materials that has invited considerable attention are the LiMO2 (M=transition metal) structures that adopt the same rhombohedral, layered O3 stacking as LiCoO2. In these structures, Co is partially or completely replaced by combinations of different transition metals, M=Mn, Ni etc. to give a whole family of materials, including LiMnO2, 1–3 LiNiO2 4–6 and LiNi1-y-zMnyCozO2 (NMC). 7,8 Alternative structures have also been generated in which the transition metal species is partially replaced with Li to give the Li2MnO3.LiMO2 ‘Li excess’ family of materials, which show extremely high energy densities, at least in the first few cycles.9,10 Within the family of layered O3 materials, LiMnO2 was initially suggested as an alternative to LiCoO2, due to the low cost and low toxicity of Mn. Although the thermodynamically stable phase of LiMnO2 at ambient conditions is orthorhombic (Pmmn),11 it was shown independently by Armstrong et al.1 and Capitaine et al.2 that a metastable phase of LiMnO2, with a layered O3 structure, could be produced by ion exchange from NaMnO2. This phase, referred to as layered LiMnO2, adopts the same oxygen stacking as LiCoO2, but with symmetry reduced from rhombohedral (R3m) to monoclinic (C2/m) as a

result of a cooperative Jahn-Teller distortion. However, a significant problem that has prevented the adoption of this material in its pristine form is that, upon delithiation, the structure undergoes a phase transformation from the layered phase to a spinel phase (Fd3m) involving the migration of Mn ions, the close packed O lattice remaining intact. The first cycle charge capacities of layered LiMnO2 were found to be 200-270 mAh/g, approaching the theoretical capacity of around 285 mAh/g. However, after the phase transformation the achievable capacity was significantly reduced and a large hysteresis in the voltage curves on charge and discharge was observed.1 After extended cycling, two voltage plateaus are formed around 4V that are characteristic of Li insertion into the tetrahedral sites of the LiMn2O4 spinel phase. The phase transformation process has been widely analyzed by a number of experimental techniques, such as XRD,1,3,12,13 electron diffraction,12,14,15 X-ray absorption spectroscopy (XAS),16,17 neutron diffraction18 and Li NMR spectroscopy18. The layered-to-spinel transformation (which can sometimes be associated with or accompanied by further disordering to form rock salt structures or domains) is a widespread phenomenon preventing the commercial use of many of these layered phases. For example, a partial or full layered-to-spinel transformation has also been proposed to occur on delithitation in a number of the O3 compounds, such as LiVO2,19 LiNiO2 after ‘mild heating’,20,21 and LiCoO2 in ‘highly strained

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particles’.22 Layered-to-spinel and rock-salt transformations occur at the surfaces of many Ni-containing layered phases.23,24 Of particular note, the layered-to-spinel transformation has also recently been found to occur in the Li excess family of materials, 25–27 where it has been proposed that the formation of domains of the spinel phase within the layered structure may be partially responsible for the voltage fade and slow rate capacity that has limited their adoption. The studies of the Li-excess materials suggest that the transition metal migration forming the spinel domain occurs in the layered LiMO2 O3 components, indicating that they may undergo similar transformation mechanisms to the LiMnO2 system. Although the thermodynamics of the end-member structures are now relatively straightforward to compute, it is non-trivial to determine how battery materials transform during electrochemical cycling. Experiments are challenging because these transformations generally occur via disordered structures (limiting the use of diffraction-based studies), the initial stages often involving the formation of very small nuclei within a bulk structure. First-principles theoretical methods also present difficulties due to the cooperative nature of many of the transitions, involving multiple atoms and requiring large system sizes. Furthermore, the electrochemically driven processes are driven by the removal/addition of atoms/ions from the material. Semi-empirical methods, while allowing larger simulated system sizes, generally do not capture the electronic structural changes that accompany migration of the transition metal ions. Our approach to attack this general problem is to specifically locate the transition states associated with the complex cooperative migration processes using a single ended hybrid eigenvector-following (EF) based method, which does not rely on prior knowledge of the final states. By coupling this method with density functional theory (DFT), electronic as well as ionic diffusional processes associated with the phase transformations can be represented, while the use of a supercell approach allows the nucleation of local defect morphologies to be captured. This method can be applied to a wide range of structural transformations that occur in technologically relevant battery materials. The facile nature of the layered-to-spinel transformation in LiMnO2 makes it a good model system to understand the underlying cation migration mechanisms occurring in many of these systems. With this insight, the eventual aim for this family of materials is to engineer their structures against the transformation, likely by doping. Previous theoretical modeling studies have helped to understand the initial mechanism by which the migration of Mn ions occurs within the structure. Reed et al.28 used DFT calculations to model putative configurations along the reaction pathway involving the migration of the Mn ions from the octahedral sites in the

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MnO6 layers to tetrahedral sites in the Li layer of Li0.5MnO2. Their studies started with Li0.5MnO2 because it was previously shown through first principles calculations that the layered Li0.5MnO2 composition was metastable with respect to the spinel phase LiMn2O4.29 In the previous model it was proposed that during the initial stage of the process, Li ions rearrange to from a tri-vacancy in the Li layer.28 This rearrangement creates a tetrahedral site in the Li above a Mn3+ ion that does not share a face with a LiO6 octahedron. Next, the Mn ion migrates from the octahedral site to the tetrahedral site, Mntet, creating a vacant site in the Mn layer, VMn. This migration occurs through the triangular oxygen face of the MnO6 octahedron, which constitutes the point of the maximum energy along the reaction path. In the final step of the process, a Li ion from the layer below the newly formed VMn migrates from an octahedral position to a tetrahedral position, Litet, below the VMn. The result of this migration process is the formation of a Litet-VMn-Mntet complex referred to as a ‘dumbbell’ defect. During the migration of MnoctMntet a charge disproportionation reaction was proposed to occur in which the migrating Mn3+ gains an electron becoming Mn2+tet and oxidizes another site from Mn3+oct Mn4+oct. They further argued that as the transformation mechanism relies on the migration of Mn ions into tetrahedral sites in the Li layer as well as the presence of Mn3+ ions as part of the charge disproportionation reaction, the driving force would depend sensitively on the Li composition, LixMnO2. At high Li compositions there would be an insufficient number of non LiO6 face sharing tetrahedral sites into which Mn can diffuse, while at low Li compositions there would be a reduction in the number of Mn3+ ions that are required for the charge disproportionation. At intermediate Li compositions, such as Li0.5MnO2, there will be a sufficient number of favorable tetrahedral sites and Mn3+ ions to produce the dumbbell defects. The prior DFT calculations focused on determining the energy at specific points along the proposed transformation pathway, which allowed comparison of relative barriers between chemical systems i.e. Li0.5MnO2,28 Li0.5CoO2,28 Li0.5VO2,30 Li0.5CrO231 and Na0.5MnO231. However, by considering only selected geometries along the migration pathway, features of the energy landscape such as shallow local minima and charge transfer processes may be lost, which are important to understand the underlying transformation mechanisms. Furthermore, the methodologies used inherently make assumptions as to the nature of the migration pathways and the degree of correlation between concerted motions of the various cations and anions. In order to provide a more faithful description of the potential energy landscape associated with the layered to spinel transformation in these materials, methods that can locate both local minima and

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transition states are therefore required. Popular methods such as nudged elastic band (NEB) 32 have routinely been used to study reaction pathways in a range of energy materials. However, the NEB approach requires knowledge of the initial and final states of the transformation pathway.

Li Rearrangement Lioct+VLi Li Mn O

Mntet VMn Litet

Figure 1: Schematic representation of defects produced in the initial layered to spinel transformation of Li0.5MnO2 from the model proposed in ref 28. Blue lines highlight vacant sites produced during the transformation. Migrating atoms are enlarged for clarity. Red (dashed) box highlights the formation of the Litet-VMn-Mntet ‘dumbbell’ defect. In this work we use single ended hybrid EF coupled with DFT to specifically locate the transition states that occur during the initial transformation process of layered Li0.5MnO2. By building on the previous computational work that has been done to model cation migrations in the layered LiMO2 systems, our main aim is to demonstrate how the hybrid EF method can be used to capture local features associated with phase transformations in this class of materials, with Li0.5MnO2 being chosen as a model system due to its important as a Li ion battery cathode material. Through the hybrid EF approach we aim to develop an understanding of how individual cation migration processes can aid the layered-tospinel transformation. We assess how the treatment of electron correlation and varying system size affect the magnitude and the nature of the energy barriers obtained from the hybrid EF approach and show that the migration of Li ions, involving both octahedral and tetrahedral local minima, aids the migration of Mn ions from octahedral to tetrahedral sites within the layered structure.

Methodology Computational Details The electronic energies and total energy gradients with respect to nuclear coordinates were calculated with DFT using the Perdew-Burke-Ernzerhof (PBE)33 spin polarized generalized gradient approximation (GGA) functional. The total energies and gradients were calculated using the VASP code 34 using the projector augmented wave (PAW) method 35

with a plane wave cut-off of 500 eV yielding an energy convergence to within 4 meV/atom. In the Mn PAW set used, the 3p electrons were treated as valence. To correct for the self-interaction error in the GGA formalism, a Hubbard U parameter (DFT+U)36 was included for the Mn ions to treat 3d correlations. Two different DFT+U methods are commonly used in the literature. The first is the rotationally invariant form proposed by Dudarev et al. 37 in which the Coulomb, U, and exchange, J, matrices are combined into a single effective U parameter, Ueff=U-J. In the second approach proposed by Liechtenstein,38 the U and J matrices are treated separately. In this work we have used the second approach, as it has previously been found for β-MnO2 that it notionally offers enhanced accuracy at little additional computational expense.39 The J value was fixed at 1 eV for all the calculations. The electronic structure of Li0.5MnO2 contains mixed Mn3+ and Mn4+ which from the work of Wang et al. 40 should have Ueff values of 4 eV and 3.5 eV respectively. An average Ueff value of 3.75 eV was chosen, corresponding to a U value of 4.75 eV with J fixed at 1 eV. To study the effect of the U parameter on the energy of Mn migration, calculations were performed both in the absence of Hubbard U interactions, i.e. pure DFT, and with varying U values of 3 eV and 7 eV (J=1 eV). All calculations were spin-polarized and were initialized in their respective ferromagnetic states. The ferromagnetic state is an approximation in the Li0.5MnO2 system, as it has been previously shown that pristine LiMnO2 adopts an antiferromagnetic ordering..41 In the iso-structural NaxMnO2 compound the nearest neighbor 90° Mn3+-O-Mn3+ exchange couplings are also found to be aniferromagnetic,42 however the magnitude of the exchange interactions in these systems are expected to be small and > , respectively. The migration of the Mn ion into the square pyramidal site (configuration e) is akin to forming an MnO6 octahedron with one of the O ligands removed, the MnO5 polyhedron having a similar splitting of the t2g and orbitals > and > , respectively. However, the removal of the oxygen ligand along the direction of the orbital lowers the energy of this orbital and reduces the overall crystal field splitting. The smaller crystal field splitting also lowers the energy of the unoccupied orbital bringing it closer to the Fermi level. An electron is then donated from the neighboring Mn3+ into the orbital of the square pyramidal Mn3+O5 producing an Mn2+ state (configuration V). Once the charge transfer process has occurred, the Mn2+ can then migrate into the tetrahedral site with a favorable electronic configuration of ∗ . The square pyramidal MnO5 configuration therefore acts as an intermediate configuration that can initially adopt a favorable d4 state with Mn3+ to allow for the initial migration, while reducing the charge transfer barrier to allow for the favorable Mn2+ d5 configuration of the tetrahedral site. The observation of a Mn3+ ion in the square pyramidal MnO5 configuration is consistent with previous studies of Mn oxides such as Na0.44MnO2,57,58 and the Li ion exchanged form Li0.44MnO2,59 that contain both square pyramidal and octahedral Mn configurations. Computational studies have shown that removal of Na ions from Na0.44MnO2 results in selective oxidation of the octahedral Mn ions from Mn3+ to Mn4+, the square pyramidal Mn ions remaining as Mn3+.60 Square pyramidal configurations with both Mn3+ and Mn2+ have also seen experimentally, for example in YBaMn2O5, a colossal magneto resistance material.61,62 Without the appropriate treatment of strong, orbital dependent on-site Mn interactions through the U parameter, the energy level splitting required to stabilize the square pyramidal MnO5 state is insufficient, and instead the migration of Mn ion occurs directly

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between the octahedral and tetrahedral sites accompanied by a gradual delocalization of the charge. This underestimate of charge localization results in a significantly smaller barrier for the transformation process as well as a significantly enhanced stabilization, around 0.4 eV, of the final dumbbell configuration. As is the case with other transition state searching methods, such as NEB that may be applied in periodic systems, the reaction pathways also depend on the system size used, as demonstrated in Figure 8. Increasing the system size from a supercell of dimension 2×3×2 (24 Mn) to 3×3×2 (36 Mn), the transformation mechanism changes from a concerted motion of Li and Mn, to sequential migration events involving the individual species, the latter presumably more accurately representing the true nucleation of the dumbbell defect within the layered Li0.5MnO2 phase. In the 2×3×2 cell, the small separation between the defect centers of only 10.64 Å along the a direction, compared to 15.97 Å for the 3×3×2 cell, results in strengthened elastic interactions between periodic images. The concerted migration of the Li and Mn into tetrahedral sites in the 2×3×2 cell results in the formation of a line defect along this direction. In the case of the 3×3×2 cell, the distance between the periodic images is large enough so that the translational symmetry constraints that arise in the smaller cell are no longer present, and the energy to nucleate individual defects is lower than to form a line defect. Similar behavior for the crossover between concerted and atom dominated processes was seen for the CdTe system by Henkelman and co-workers using the generalized solid state nudged elastic band approach.63 In this work they allowed the atomic and cell (unit cell parameters and internal angles) degrees of freedom to vary and found that for small to medium cell sizes, concerted processes involving bulk rearrangements and line defects respectively were favored over atom-dominated nucleation events. For larger cells they found that there was a crossover point after which atom dominated nucleation events were favored over concerted motions. In the current work the lattice parameters were fixed throughout the transformation process. However, the difference in the lattice parameters of the final states after subsequent geometry optimization was small, suggesting that the initial migration pathways do not involve a significant variation in the cell geometry. This result is most likely the case because the backbone of the structure is based on a closed packed oxygen network that is common to both the layered LiMnO2 and spinel LiMn2O4 phases. With the fundamental understanding about the migration processes in Li0.5MnO2 gained by the current approach, a key challenge that remains is to devise strategies that increase the transition metal migration barriers so as to kinetically stabilize the layered Li0.5MnO2 structure. An approach that has been widely proposed is to substitutionally dope the Mn site with other metal species. The effect on the Mn migration barrier can be studied by selectively substituting dopants in different

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coordination environments in the transition metal layer around the migrating Mn. In the current hybrid EF approach, as with other single ended transition state searching methods, the location of the transition state constitutes the most computationally demanding part of the reaction pathway. However, a key benefit of this approach is that the transition state geometries located for the pristine Li0.5MnO2 structure should provide good starting points with which to explore the effect of the transition metal dopants. By starting the doped transition state searches from the un-doped Li0.5MnO2 geometries, the computation expense should be minimized, allowing for the potential screening of the effect on the migration barrier of a large range of dopants. Dopants that significantly increase the Mn migration barrier without adversely affecting the Li migration barrier can then be selected for experimental testing. The effect of dopant species on the migration barriers in Li0.5MnO2 will be a focus of a future study.

Conclusions Hybrid eigenvector-following (EF) methods coupled with periodic density functional theory allows the individual migration mechanisms associated with the initial part of the layered to spinel transformation in Li0.5MnO2 to be determined and rationalized. By building upon the understanding that has been gained about the layered to spinel transformation from previous computational studies, the use of the hybrid EF approach in the current study was found to provide a more efficient and unbiased description of the initial transformation of Li0.5MnO2 involving multiple transition states and local minima. Li ion migration out of the octahedral sites in the structure was found to occur through a divacancy mechanism in which both tetrahedral and octahedral sites served as local minima along the diffusion pathway. In contrast to previous reports, the initial Mn migration from octahedral sites in the transition metal layers to the Li layer was found to be aided by Li diffusion into the tetrahedral sites. Further migration of the Mn ion to a tetrahedral site in the Li layer was found to occur through an intermediate square pyramidal configuration MnO5, followed by an independent Mn3+ Mn2+ charge transfer mechanism. An appropriate treatment of Mn d-electron interactions with a Hubbard U model was found to be essential to describe the intermediate MnO5 configuration and charge transfer process. The transformation mechanism did not change significantly with varying U, however by removing the U parameter completely, the independent MnO5 and charge transfer steps were no longer observed, and instead a gradual delocalization of the charge was observed. The ability to capture the ionic and electronic diffusion processes with the current hybrid EF method coupled with DFT, should prove to be useful for studying other potential Li ion cathode materials in which Li ion conduction is accompanied by

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charge transfer effects, such as small polaron diffusion. It was shown that the supercell size used in the current EF calculations had an important impact on the calculated migration barriers. In large cells, independent Li and Mn migrations were favored, whereas in a small cell, only cooperative Li and Mn migration was found to be present, with a significantly larger activation barrier.

for Functional Nanomaterials, Brookhaven National Laboratory, which is supported by the U.S. Department of Energy, Office of Basic Energy Sciences, under Contract No. DE-AC02-98CH10886. I.D.S would like to acknowledge funding from the Geoffrey Moorhouse Gibson Studentship in Chemistry from Trinity College Cambridge. S.C would like to acknowledge Carl Tryggers Stiftelse for Vetenskaplig Forskning (CTS) and Rajeev Ahuja.

The findings from this current work on the layered to spinel transformation in Li0.5MnO2, as well as the effects of the treatment of Mn d-electron interactions and system cell size, should prove useful in studying the phase transformation mechanisms and diffusional properties of a range of technologically interesting energy materials, including the related layered phases. In particular, the hybrid eigenvector-following approach allows the complex structural rearrangements that often occur in cycling battery electrode materials to be followed without prior knowledge of the final structures. The method is expected to be particularly valuable for the study of electrode materials, since the delithiation pathways (or cation removal more generally) often involve the formation of a series of metastable structures. The reversibility of the electrode chemistry is then highly dependent on the kinetics of the various phase transformations, and the kinetic stabilities of the metastable states. Examples of such systems include the lithium iron silicates, the lithium-excess layered materials and many conversion chemistries.

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Via our membership of the UK's HPC Materials Chemistry Consortium, which is funded by EPSRC (EP/L000202), this work made use of the facilities of HECToR and ARCHER, the UK's national high-performance computing service, which is funded by the Office of Science and Technology through EPSRC's High End Computing Programme. Research was also carried out at the Center

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ASSOCIATED CONTENT (Supporting Information [S1) Plot of the variation in integrated differential spin density versus sphere radius around Mn S2) Density of states plots for Li0.5MnO2 structure in Figure 2 S3) Projected density of states plot for diffusing Mn ion in configurations d), e) and f) in Figure 5. “This material is available free of charge via the Internet at http://pubs.acs.org.”

AUTHOR INFORMATION Corresponding Author * Email: [email protected]

Present Addresses Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK.

Notes The authors declare no competing financial interest.



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