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Defect physics and chemistry in layered mixed transition metal oxide cathode materials: (Ni,Co,Mn) vs. (Ni,Co,Al) Khang Hoang, and Michelle Johannes Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.5b04219 • Publication Date (Web): 08 Feb 2016 Downloaded from http://pubs.acs.org on February 9, 2016

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Chemistry of Materials

Defect physics and chemistry in layered mixed transition metal oxide cathode materials: (Ni,Co,Mn) vs. (Ni,Co,Al) Khang Hoang∗,† and Michelle Johannes‡ Center for Computationally Assisted Science and Technology, North Dakota State University, Fargo, ND 58108, United States, and Center for Computational Materials Science, Naval Research Laboratory, Washington, D.C. 20375, United States E-mail: [email protected]

Abstract Although layered lithium transition-metal oxides with different compositions of (Ni,Co,Mn) [NCM] or (Ni,Co,Al) [NCA] have been used in commercial lithium-ion battery cathodes, their defect physics and chemistry is still not well understood, despite having important ramifications for cycling properties, particularly capacity fade. Herein we report a hybrid density functional study of the crystal and electronic structures of and intrinsic point defects in the compositions LiNi1/3 Co1/3 Mn1/3 O2 (NCM1/3 ) and LiNi1/3 Co1/3 Al1/3 O2 (NCA1/3 ) which also serve as model compounds for NCM and NCA. We find that the transition metals can exist in different charge and spin states at different lattice sites. In NCM1/3 , nickel/lithium antisite pairs, i.e., NiLi -LiNi , are estimated to be about 3% in samples prepared at 1000◦ C. In NCA1/3 , in addition to nickel ∗

To whom correspondence should be addressed Center for Computationally Assisted Science and Technology, North Dakota State University, Fargo, ND 58108, United States ‡ Center for Computational Materials Science, Naval Research Laboratory, Washington, D.C. 20375, United States †

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antisites NiLi , aluminum antisites AlLi can also occur with a very high concentration. The detrimental AlLi defect has a high energy except when it is located between two Al atoms at the transition-metal sites both above and below the lithium layer, i.e., when the concentration of Al is high enough that significant amounts exist in three successive layers. Our results thus provide a natural explanation for why the observed improvement in the electrochemical performance of NCA at low Al concentrations gives way to drastically decreased performance beyond about 10%. The effects of substituting Al for Mn on the lithium migration and overall voltage profile are also discussed. KEYWORDS: layered oxides, defects, first-principles, hybrid functional

Introduction LiNi1/3 Co1/3 Mn1/3 O2 , hereafter denoted as NCM1/3 , is a commercially available lithium-ion battery cathode material, having alternate lithium and transition-metal (TM) oxide layers. 1 NCM1/3 is an example of layered oxides thought to demonstrate structural stabilization via both electronic stabilization and structural “pillaring” that prevents the TM oxide layers from collapsing or sliding. 2,3 The former is achieved by having a mixture of heterovalent ions Ni2+ , Co3+ , and Mn4+ that are Jahn-Teller inactive, and the latter by having just a few percent cation disorder in the lattice. A substitution of Al for Mn, resulting in LiNi1/3 Co1/3 Al1/3 O2 , denoted as NCA1/3 , has also been reported and shown to cycle successfully. 4–6 These two materials can be regarded as special cases of LiNix Coy Mnz O2 (NCM, also known as NMC) and LiNix Coy Alz O2 (NCA), where x + y + z = 1; some of which are now available in commercial lithium-ion batteries, including those for vehicle applications. 7–9 A detailed first-principles study of NCM1/3 and NCA1/3 not only can elucidate their defect physics and chemistry but also help shed light on their electrochemical properties and those of the related materials. Experimentally, the cation disorder in NCM1/3 , which appears to be solely Ni/Li, is reported to be about 1−6% . 10–17 The cation disorder is also observed even in lithium-rich 2


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NCM1/3 , i.e., Li1+x (Ni1/3 Mn1/3 Co1/3 )1−x O2 , although with less than 2%. 18 As for NCA1/3 , it is reported that this material has a lower specific capacity and a higher irreversible capacity compared to NCM1/3 . 5,6 Unlike the Mn analogue, NCA1/3 is not widely studied and its electrochemical properties are much less well understood. First-principles density-functional theory (DFT) studies of NCM1/3 and NCA1/3 have been carried out by several research groups and mainly focused on the crystal and electronic structures. 19–22 A number of point defects in NCM1/3 are studied by Lee and Park, 23 using interatomic-potential simulations, and by Park, 24 using DFT within the generalized gradient approximation. 25 These methods are, however, known to have limited predictive power in TM-containing materials. We herein present a detailed study of the bulk properties and defect physics and chemistry in NCM1/3 and NCA1/3 , following a computational approach based on first-principles defect calculations developed for battery electrode materials. 26,27 Our study uses a hybrid DFT/Hartree-Fock method which has been shown to be very promising in reproducing the correct physics of complex oxides, especially the electronic structure near the band edges and the charge and spin states of the TM ions. 27–29 We search for low-energy structural models for NCM1/3 and NCA1/3 using an heuristic approach; they are then used as reference structures for defect calculations. The structure and energetics of all possible intrinsic point defects in the materials are investigated and low-energy defects are identified; lithium migration is also investigated. Our estimated degree of the cation disorder in NCM1/3 is in excellent agreement with experiments. The poor cyclability of NCA1/3 can be understood partly in terms of the very low formation energy of nickel and aluminum antisite defects; the latter is caused by the cross-layer interaction of the Al 3p states and can only occur in NCA at moderate to high Al content when neighbors are available in both adjacent layers.

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Methodology Our calculations are based on DFT, using the Heyd-Scuseria-Ernzerhof (HSE06) screened hybrid density functional, 30,31 the projector augmented wave method, 32,33 and a plane-wave basis set, as implemented in the Vienna Ab Initio Simulation Package (VASP). 34–36 The Hartree-Fock mixing parameter and the screening length are set to the standard values of 0.25 and 10 ˚ A, respectively. Bulk and defect calculations for NCM1/3 and NCA1/3 are carried out using 108-atom supercell models, unless otherwise noted, and a plane-wave basis-set cutoff of 500 eV; spin polarization is included. Convergence with respect to self-consistent iterations is assumed when the total-energy difference between cycles is less than 10−4 eV and the residual forces are less than 0.01 eV/˚ A. Integrations over the Brillouin zone are carried out using the Γ point, except in the calculations of the electronic density of states where a 3×3×2 k-point mesh is employed. In the defect calculations, the lattice parameters are fixed to the calculated values of the perfect bulk supercells but all the internal coordinates are relaxed. These settings are thus the same as those in our previous works 27,29 on layered LiCoO2 , LiNiO2 , and LiMnO2 to ensure the transferability of our calculations across the compounds. The likelihood of a point defect or defect complex X in effective charge state q being incorporated into a crystal is characterized by its formation energy, defined as 37,38 E f (Xq ) = Etot (Xq ) − Etot (bulk) −

X

ni µi + q(Ev + µe ) + ∆q ,

(1)

i

where Etot (Xq ) and Etot (bulk) are the total energies of the defect and bulk supercells, respectively; ni denotes the number of atoms of species i that have been added (ni > 0) or removed (ni < 0) to form the defect; µi is the atomic chemical potential, representing the energy of the reservoir with which atoms are being exchanged, referenced to the total energy per atom of bulk metals and an isolated O2 molecule at 0 K. µe is the electronic chemical potential, i.e., the Fermi level, representing the energy of the electron reservoir, referenced 4


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to the valence-band maximum (VBM) in the bulk (Ev ). ∆q is the correction term to align the electrostatic potentials of the bulk and defect supercells and to account for finite-size effects on the total energies of charged defects. 39,40 The atomic chemical potentials are subject to thermodynamic constraints. For example, the stability of NCM1/3 requires 1 µLi + (µNi + µCo + µMn ) + 2µO = ∆H f (NCM1/3 ), 3

(2)

where ∆H f is the formation enthalpy. Similarly, the stability condition for the host compound NCA1/3 is 1 µLi + (µNi + µCo + µAl ) + 2µO = ∆H f (NCA1/3 ). 3

(3)

Equation (2) or (3) places a lower bound on the value of µi . The upper bound of µi is zero as one needs to avoid precipitating bulk metals or forming O2 gas; i.e., ∆H f (NCM1/3 ) ≤ µi ≤ 0 in NCM1/3 or ∆H f (NCA1/3 ) ≤ µi ≤ 0 in NCA1/3 . Stronger bounds on µi are imposed by competing Li−Ni−Co−Mn−O or Li−Ni−Co−Al−O phases. For example, the stability of NCA1/3 against the formation of the competing phase LiAlO2 requires µLi + µAl + 2µO ≤ ∆H f (LiAlO2 ).

(4)

By taking into account all the constraints, one can determine the range of µi values, bounded in a 4-polytope in the 4-dimensional atomic chemical potential space, in which the host NCM1/3 or NCA1/3 is thermodynamically stable. Since the construction of this 4-polytope is not practical, we select only sets of the chemical potentials that are likely to reflect actual experimental conditions during materials preparation. We note that the equivalent of a stability 4-polytope in quintinary compounds is a polygon in ternaries or a polyhedron in quaternaries. 26,29 Also note that the energies in Eqs. (2)−(4) should, in principle, be free

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energies; however, for solid phases the temperature and pressure dependence can be neglected in a first approximation. 38 Finally, the electronic chemical potential, i.e., the Fermi level of NCM1/3 or NCA1/3 , under thermodynamic equilibrium can be calculated self-consistently according to charge neutrality condition which involves the equilibrium concentrations of all intrinsic defects and any impurities and free carriers present in the material. In other words, the defect formation energy [Eq. (1)] at the equilibrium Fermi level can be computed for a given set of the atomic chemical potentials. Defects with low formation energies will easily form and occur in high concentrations, e.g., during materials preparation at high temperatures. In thermodynamic equilibrium, the concentration of a defect is given by the expression

c = Nsites Nconfig exp

−E f kB T

,

(5)

where Nsites is the number of high-symmetry sites in the lattice per unit volume on which the defect can be incorporated, Nconfig is the number of equivalent configurations (per site), and kB is Boltzmann’s constant. 37 Defects, especially the immobile ones, are expected to remain in NCM1/3 and NCA1/3 even after cooling to room temperature. During lithium extraction, i.e., when the materials are being used in a battery, one can assume that only lithium (and certain other elements such as oxygen, if the delithiation mechanism involves oxygen release) is exchanged with the environment. This assumption, in fact, results in a more general formulation of the deintercalation voltage as described in Ref. 27.

Results and Discussion Bulk Properties. Figure 1 shows the 108-atom supercell models for NCM1/3 and NCA1/3 . In both structures, the Ni:Co:Mn(Al) ratio in each TM layer remains 1:1:1. There is a longrange order (LRO) in the TM layers in the case of NCM1/3 that is similar to that in some structural models for NCM1/3 proposed previously, 19,20,24 although the stacking along the c6


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Figure 1: Supercell models for (a) NCM1/3 and (b) NCA1/3 and (c) the arrangement of the ions in the transition-metal layer in NCM1/3 . Large spheres are Li; medium spheres are Ni (green), Co (yellow), and Mn (orange) or Al (purple); and small spheres are O. The arrangement of the ions in each transition-metal layer in NCA1/3 is somewhat disordered.

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axis may be different. In NCA1/3 , the arrangement of the ions in the TM layers is somewhat disordered. Both supercell models are constructed from a hexagonal cell of LiCoO2 with twothirds of the Co ions replaced by Ni and Mn (or Al). The structure of NCA1/3 is obtained by starting with a structure similar to NCM1/3 and switching the positions of the atoms on the TM sublattice until no lower-energy atomic arrangements can be found. All lowenergy NCA1/3 structures are found to contain Al−Al−Al atomic chain segments in the TM layers, which implies a strong and directional Al 3p−Al 3p interaction. After full structural optimization, the NCM1/3 supercell remains hexagonal with the calculated lattice constants a = b = 8.56 ˚ A and c = 14.23 ˚ A and a cell volume of 33.45 ˚ A3 per formula unit (f.u.), in agreement with experimental data. 1,6 The TM ions in NCM1/3 are stable as Ni2+ (with a calculated magnetic moment of 1.69 µB ), low-spin Co3+ (0 µB ), and Mn4+ (3.00 µB ). The A (Mn−O). The relaxed A (Co−O), and 1.91 ˚ A (Ni−O), 1.92 ˚ bond lengths are about 2.04 ˚ NCA1/3 supercell is distorted with the lattice parameters a = 8.49 ˚ A, b = 8.33 ˚ A, c = 14.15 ˚ A, α = 90.0◦ , β = 88.9◦ , and γ = 119.4◦ ; the cell volume is 32.29 ˚ A3 /f.u., compared to A3 /f.u. 6 The TM ions in NCA1/3 are found to be stable as the experimental value of 32.63 ˚ low-spin Ni3+ (with a magnetic moment of 0.84 µB ) and low-spin Co3+ (0 µB ). The Ni3+ ion is Jahn-Teller active with the two long Ni−O bonds of about 2.06 ˚ A and four short bonds of 1.89 ˚ A; the average Ni−O and Al−O bond lengths are 1.92 ˚ A and 1.91 ˚ A, respectively. The formation enthalpy (at 0 K) of NCM1/3 is calculated to be −7.38 eV/f.u. with respect to the elemental metals and O2 gas or −0.22 eV/f.u. with respect to layered LiNiO2 , LiCoO2 , and LiMnO2 . For comparison, the standard formation enthalpy is measured to be −6.73 or −6.76 eV/f.u. 13 For NCA1/3 , the formation enthalpy is −8.19 eV/f.u. with respect to the elemental metals and O2 gas or −0.01 eV/f.u. with respect to LiNiO2 , LiCoO2 , and tetragonal LiAlO2 . We find that different stackings in NCM1/3 are almost degenerate in energy and the ferrimagnetic configuration, in which the spins of Ni2+ and Mn4+ are antiparallel, is only

Defect Physics and Chemistry in Layered Mixed ... - ACS Publications

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