Insights into the Nature and Evolution upon Electrochemical Cycling of

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Insights into the Nature and Evolution upon Electrochemical Cycling of Planar Defects in the β‑NaMnO2 Na-Ion Battery Cathode: An NMR and First-Principles Density Functional Theory Approach Raphael̈ e J. Clément,† Derek S. Middlemiss,†,‡ Ieuan D. Seymour,† Andrew J. Ilott,§,∥ and Clare P. Grey*,†,∥ †

Department Department § Department ∥ Department ‡

of of of of

Chemistry, Chemistry, Chemistry, Chemistry,

University of Cambridge, Cambridge CB2 1EW, U.K. University of Warwick, Coventry CV4 7AL, U.K. New York University, New York, New York 10003, United States Stony Brook University, Stony Brook, New York 11790-3400, United States

S Supporting Information *

ABSTRACT: β-NaMnO2 is a high-capacity Na-ion battery cathode, delivering ca. 190 mAh/g of reversible capacity when cycled at a rate of C/20. Yet, only 70% of the initial reversible capacity is retained after 100 cycles. We carry out a combined solid-state 23Na NMR and first-principles DFT study of the evolution of the structure of β-NaMnO2 upon electrochemical cycling. The assynthesized structure contains planar defects identified as twin planes between nanodomains of the α and β forms of NaMnO2. GGA+U calculations reveal that the formation energies of the two polymorphs are within 5 meV per formula unit, and a phase mixture is likely in any NaMnO2 sample at room temperature. 23 Na NMR indicates that 65.5% of Na is in β-NaMnO2 domains, 2.5% is in α-NaMnO2 domains, and 32% is close to a twin boundary in the as-synthesized material. A two-phase reaction at the beginning of charge and at the end of discharge is observed by NMR, consistent with the constant voltage plateau at 2.6−2.7 V in the electrochemical profile. GGA+U computations of Na deintercalation potentials reveal that Na extraction occurs first in α-like domains, then in β-like domains, and finally close to twin boundaries. 23Na NMR indicates that the proportion of Na in α-NaMnO2-type sites increases to 11% after five cycles, suggesting that structural rearrangements occur, leading to twin boundaries separating larger α-NaMnO2 domains from the major β-NaMnO2 phase.

1. INTRODUCTION The first studies on Na−Mn−O ternary oxides for rechargeable sodium-ion batteries date back to the 1980s.1 Since then, and owing to the rich phase diagram of NaxMnO2, a variety of NaxMnO2 structures with different sodium contents have been synthesized2−4 and studied in electrochemical Na cells.5−8 NaMnO2 is a layered material consisting of alternating MnO2 and Na sheets, and it exists in two polymorphic forms, denoted α and β. While the layers are flat in the α-NaMnO2 polymorph with monoclinic symmetry (C2/m space group), they are corrugated (zigzag-like) in β-NaMnO2 with orthorhombic symmetry (Pmnm space group), as shown in Figure 1. The α form is the low-energy, thermodynamically stable phase under ambient conditions.2 Intergrowths between the α- and β-NaMnO2 structures have been reported.10,11 A recent transmission electron microscopy (TEM) and synchrotron X-ray diffraction (XRD) study by Abakumov et al.11 showed that the ordering of planar defects in α- and β-NaMnO2 could be described by a superspace model, the twin planes forming quasi-periodic sequences introducing modulations in the arrangement of the NaMnO2 layers. Recent reports have suggested that these coherent intergrowths have a © 2016 American Chemical Society

Figure 1. Experimental crystal structures of the two polymorphs of NaMnO2: (a) monoclinic α-NaMnO2 (C2/m space group)2 and (b) orthorhombic β-NaMnO2 (Pmnm space group).9 The axis of the cooperative Jahn−Teller distortion of the Mn3+ ions is indicated with a dashed double-headed arrow.

strong influence on the magnetic interactions in the system and on the magnetoelectric coupling of the bulk compound.12,13 The α- and β-NaMnO2 structures exhibit triangular and folded triangular spin lattices, respectively, with frustrated Received: July 27, 2016 Revised: October 6, 2016 Published: October 6, 2016 8228

DOI: 10.1021/acs.chemmater.6b03074 Chem. Mater. 2016, 28, 8228−8239

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Chemistry of Materials

assisted by first-principles hybrid density functional theory (DFT)/Hartree−Fock (HF) calculations of the 23Na NMR parameters (hyperfine shifts, δiso, and the second-order quadrupolar induced shift, δQIS). Two structures were built (denoted Mixed Cell 1 and Mixed Cell 2) that contain twin boundaries between α- and β-type structural domains, as shown in Figure 2a,b, to permit calculations of magnetic couplings,

antiferromagnetic (AFM) (next-)nearest-neighbor Mn3+−Mn3+ interactions within the MnO2 layers, and negligible interlayer interactions. A magnetic susceptibility and neutron powder diffraction study of α-NaMnO2 revealed the presence of ferroorbital ordering, with all Jahn−Teller elongated Mn−O bonds pointing along the dz2 orbitals of the Mn3+ ions, as indicated in Figure 1a. The resulting cooperative distortion of the crystal structure leads to inequivalent magnetic exchange interactions in the MnO2 planes. The dominant direct-exchange interactions (J1) perpendicular to the ferro-orbital ordering direction form zigzag -Mn-O-Mn- AFM chains, and the weaker interchain AFM interactions (J2) along the other two directions of the triangular lattice, are frustrated.14 An early study by Mendiboure et al.1 investigated the electrochemical (de)intercalation behavior of the two polymorphs of NaMnO2 in a Na cell, the authors reporting very narrow reversible (de)intercalation windows for α-Na1−xMnO2 (0 ≤ x ≤ 0.22) and β-Na1−xMnO2 (0 ≤ x ≤ 0.15). The intercalation behavior of the α form was recently revisited by Ma et al., who showed, using an electrolyte different from the one used previously, that 0.8 Na could be extracted and reversibly inserted back upon electrochemical cycling, corresponding to a reversible capacity of 197 mAh/g.6 Some of us subsequently studied the electrochemistry and the structural changes occurring upon cycling of the β-NaMnO2 cathode material, using XRD and solid-state nuclear magnetic resonance (ssNMR), and reported that the as-synthesized β-NaMnO2 phase exhibits a significant proportion of structural defects/twin planes.7 Yet, to the best of our knowledge, no study has been undertaken to understand the exact nature of the planar defects and their impact on the sodium (de)intercalation mechanism in NaMnO2. This paper builds upon Abakumov et al.’s recent TEM findings,11 and on our previous work on the β-NaMnO2 cathode,7 and consists of an in-depth analysis of the 23Na ssNMR data obtained for the as-synthesized β-NaMnO2 material and at different points along the first electrochemical cycle. Ex situ ssNMR has proved to be a very useful tool for the investigation of Li- and Na-ion battery materials.7,15−17 It can probe short-range structural changes occurring upon extraction and reinsertion of the electrochemically active species, is sensitive to changes in transition metal oxidation states, and, unlike diffraction methods, allows the investigation of highly disordered or amorphous phases arising upon electrochemical cycling. In the present work, a detailed analysis of the local environments formed at the boundary between domains of α- and β-NaMnO2, using 23Na ssNMR, gives insight into the nature of the stacking faults. 23Na ssNMR allows us to extract information on the populations of the various Na local environments present in the pristine material, as well as how these populations evolve as Na is electrochemically extracted from and reinserted into the material. As reported in a number of studies of paramagnetic materials,18,19 the main contribution to the 23Na isotropic shift (δiso) in NaxMnO2 compounds is the Fermi contact shift, which arises from the hyperfine (paramagnetic) interactions between the Na nucleus and unpaired electrons on nearby Mn spins. For an I = 3/2 quadrupolar nucleus such as 23Na, the interaction between the nuclear electric field gradient (EFG) and the external magnetic field leads to a further broadening of the spectrum and to a shift of the 23Na Larmor frequency due to second-order effects. The assignment of the complex paramagnetic 23Na NMR spectra of these disordered systems is

Figure 2. Diagrams of the two mixed α/β-NaMnO2 structures considered here with twin boundaries between α and β domains: (a) Mixed Cell 1 and (b) Mixed Cell 2. The structures of the ideal (c) α-NaMnO2 and (d) β-NaMnO2 polymorphs are shown for comparison. Only Na atoms are represented here, and each color is associated with a particular Na local environment. The dashed boxes depict the projection of the unit cells used in first-principles computations.

hyperfine shifts and quadrupolar parameters for representative local environments. The ideal structures of the α-NaMnO2 and β-NaMnO2 polymorphs are shown in Figure 2c,d, respectively, for comparison. Only the Na atoms are drawn in these figures in order to show the alternating regions of flat and corrugated layers more clearly (diagrams depicting all of the different atomic species in the various NaMnO2 structures are shown in Figure S1 in the Supporting Information (SI)). The different colors of the Na+ ions correspond to inequivalent Na environments. The hyperfine parameters provided by first-principles NMR calculations are obtained at 0 K from cells containing ferromagnetically aligned open-shell Mn ions. To compare this data with experimental data acquired at finite temperature, we require knowledge concerning the magnetic properties of the material and the nature and size of any magnetic couplings that persist in the paramagnetic state. This is non-trivial in a disordered system where the local magnetic interactions may differ noticeably from those of the bulk: specifically here the magnetic couplings in α domains, in β domains, and in the vicinity of a twin boundary may be very different. These couplings have a direct effect on the Na chemical shifts. To address this issue, we determine the local magnetic properties from Monte Carlo simulations of an Ising spin model of the magnetic lattice using the Mixed Cell 1 structure. We extract magnetic scaling factors, Φ, for different magnetic sites, which relate the saturated magnetic moments at 0 K to the thermal averaged values of the magnetic moments of individual Mn spins at the temperature of the NMR experiments (320 K).15 These values 8229


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Hubbard U model35,36 within the rotationally invariant formalism proposed by Liechstenstein et al.37 to correct for the known deficiencies of pure functionals for highly localized 3d states.38 The plane-wave energy cutoff was set to 520 eV. An effective Hubbard parameter Ueff = U − J = 3.9 eV, where U and J are the effective on-site Coulomb and exchange parameters (J = 1 eV), was chosen for Mn in line with previous work on NaxMnO2.39 Additional computational details are presented in the SI. 2.4. Magnetic Susceptibility Measurements and Computation of the Temperature-Dependent Magnetic Scaling Factor Φ(T). 2.4.1. Scaling of the First-Principles 23Na NMR Parameters. The method adopted here to compare the 23Na NMR parameters obtained from first principles with the experimental NMR data was described in a previous study15 and is further discussed in the SI. Briefly, first-principles 23Na Fermi contact shifts are obtained in ferromagnetic cells (all Mn3+ spins are co-aligned), corresponding to the saturated magnetic moment Msat. The computed shifts are subsequently scaled to a value consistent with the magnetic state of the system at the temperature of the NMR experiments, using a magnetic scaling factor of the form

are compared with the scaling factors obtained from experimental susceptibility measurements of β-NaMnO2. Of note, this is the first time that such an approach is used to predict hyperfine NMR parameters in a system containing inequivalent paramagnetic metal (here Mn) local environments. 23 Na Fermi contact NMR shifts can be decomposed into additive bond pathway contributions (BPCs) from nearby Mn spins, using a method developed by Middlemiss et al.20 Once individual shift contributions for all possible Mn−O−Na interactions in the structure are known, the total shift of a variety of Na environments, differing in their numbers and types of Mn−O−Na interactions, can be reconstructed. It is shown here that the different shift contributions computed in the ideal α-NaMnO2 and β-NaMnO2 structures allow the determination of the total Fermi contact shifts of the different local environments present in NaMnO2-type materials, e.g., Na(α), Na(β), Na(1), Na(2), Na(pseudo-α), and Na Na(pseudo-β), using the notation introduced in Figure 2. In turn, the different shift contributions are used to identify the various local environments in the real material, based on the Na resonances observed in the NMR spectra, the occupation of which can then be quantified from integrated NMR intensities. The energetics of stacking fault formation in β-NaMnO2 are evaluated from first principles to help understand the propensity for structural intergrowths in NaMnO2-type materials. Finally, Na (de)intercalation potentials are computed for the different Na sites created when structural defects are introduced in the structure to assist the interpretation of the 23Na NMR data at the beginning of charge.

Φ(Texp) =

Msat

(2)

where ⟨M(Texp)⟩ is the temperature-dependent average magnetic moment evaluated at the sample experimental temperature, Texp. Here, Texp was set to 320 K to account for frictional heating caused by fast (60 kHz) rotation of the NMR rotor. As discussed below, Φ was calculated in two different ways: a bulk value was obtained from the experimental magnetic susceptibility of the material, and site-specific scaling factors (i.e., accounting for inequivalent Mn environments in the material) were determined from Monte Carlo simulations. 2.4.2. Bulk Φ(T) from Experimental Magnetic Susceptibility Measurements. The field-cooled (FC) DC magnetic susceptibility of β-NaMnO2 was recorded on a commercial magnetic property measurement system (MPMS) over the temperature range 2−350 K. In addition, the magnetic susceptibility of a different sample of β-NaMnO2 was measured on a physical property measurement system (PPMS) between 700 and 300 K using vibrating sample magnetometry (VSM). All measurements were performed under an external field of 1000 Oe. A bulk value for the magnetic scaling factor Φ presented in eq 2 can be derived from the experimental molar magnetic susceptibility χm(T):

2. EXPERIMENTAL DETAILS AND METHODOLOGY 2.1. 23Na Solid-State NMR Experiments. A series of 23Na solidstate NMR spectra obtained at different points along the first electrochemical cycle of β-NaMnO2 was presented in earlier work7 and is studied in more detail here. Experimental details on the preparation of the electrochemically cycled samples and on the acquisition of the NMR data are given in our previous publication7 and in the SI. The observed shift (δobs) is the sum of the isotropic (hyperfine) shift, which has a linear dependence on the external magnetic field strength, B0, and of the second-order quadrupolar shift, which has an inverse dependence on B0:

δobs = δiso + δQIS

⟨M(Texp)⟩

Φ(T ) =

(1)

B0 χm (T ) gμB SNA

(3)

where B0 is the external magnetic field, S is the formal spin of the transition metal species, g is the experimental g-value for NaMnO2, μB is the Bohr magneton, and NA is Avogadro’s number. A derivation of eq 3, starting from the final expression obtained by Kim et al.,15 can be found in the SI (eq S4) along with the experimental values used in this work. 2.4.3. Site-Specific Φ(T) from Monte Carlo Simulations of the Magnetism of NaMnO2 Spin-Lattices. In order to assess the effect of α/β intergrowth on the magnetic properties of NaMnO2, the magnetism of the Mixed Cell 1 structure containing twin planes separating nanodomains of α- and β-NaMnO2 (see Figure 2a) was simulated using a modified form of the Monte Carlo code developed by Harrison and co-workers.40−42 The simulations considered the three nearest-neighbor Ja magnetic couplings between pairs of Mn3+ spins in α and β domains in the Mixed Cell 1 structure, as shown in Figure S2 in the SI. The Ja constants were obtained from hybrid HF/DFT calculations in the α-NaMnO2 and β-NaMnO2 structures. The code is capable of simulating both cation and magnetic disorder and the underlying theory can be found in Harrison et al.’s previous work.40 The present version of the code implements an Ising-type magnetic model and will be presented in a forthcoming publication. Further details on the methodology and experimental parameters used here are given in the SI. The scaling factors for inequivalent Mn environments in the Mixed Cell 1 structure were obtained from the

2.2. Hybrid Density Functional Theory (DFT)/Hartree−Fock (HF) calculations. Hybrid DFT/HF calculations were performed in the spin-unrestricted approach to determine NMR parameters and Ja magnetic coupling strengths in NaMnO2-type structures. NMR calculations were carried out on experimental (EXP) and first-principles optimized (OPT) structures, the latter resulting from full optimizations of the atomic positions and cell parameters. The CRYSTAL09 all-electron linear combination of atomic orbital code was used21,22 and two spin-polarized exchange-correlation functionals based upon the B3LYP form23−26 were applied, with Fock exchange weights of F0 = 20% (B3LYP or H20) and 35% (H35). Full details of the hybrid DFT calculations, including basis sets and numerical parameters, are presented in the SI. 2.3. GGA+U Calculations of Formation Energies and Intercalation Potentials in NaMnO2-Type Structures. Spinunrestricted solid-state DFT simulations27,28 of formation energies and intercalation potentials were performed in the Vienna Ab Initio Simulation Package (VASP5.2).29−31 The projector-augmented wave (PAW) approach32,33 was used to describe the electron−ion core interaction. Full optimizations of the atomic positions and cell parameters, and total energy calculations, were performed without applying symmetry constraints. The Perdew−Burke−Ernzerhof (PBE) exchange-correlation functional34 was used throughout, applying the 8230


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material (i.e., every four layers on average).7 For the sample obtained after five charge/discharge cycles, about 54% of all Na+ ions occupy β-like sites, 27% are in the vicinity of a twin boundary, 10% occupy α-like sites, and 9% are in diamagnetic environments (e.g., in electrolyte decomposition products). Hence, in the cathode material itself, 59% of Na+ ions are in Naβ sites, 30% are in NaSF sites, and 11% are in Naα environments after five cycles, indicating that the concentration of Na+ ions in α-like domains increases as Na is extracted from and reinserted into β-NaMnO2. 3.1.2. Assignment of the 23Na NMR Signals from FirstPrinciples Calculations. How Do Stacking Faults Influence the Magnetism of β-NaMnO2? In order to compute the hyperfine shifts, we must first derive appropriate magnetic scaling factors for the various Mn local environments in the disordered NaMnO2 structure. The first approach is to determine an average of these values from experimental measurements of bulk magnetic susceptibility data obtained for a powder sample of β-NaMnO2 (see Figure S3 in the SI). From this data, a bulk magnetic scaling factor Φ = 6.64 × 10−3, corresponding to an average over all Mn sites in the material, was computed at 320 K and at an external field of 4.7 T using eq 3. Site-specific scaling factors for different Mn spins in α-like, β-like nanodomains, and close to a twin boundary (Φα, Φβ, and ΦSF respectively) were obtained from Monte Carlo simulations on the Mixed Cell 1 structure (see Figure 2a). In addition to the structure, the Monte Carlo simulations require as input the magnetic couplings between nearby magnetic ions. Four sets of magnetic coupling constants were derived (as presented in Table S2 in the SI) from the α- and β-NaMnO2 experimental (EXP) structures2,9 on the one hand, and from the structures obtained after a first-principles optimization (OPT) on the other hand, using two exchange-correlation functionals (H20 and H35). Separate Monte Carlo simulations were performed using each of the four different sets of coupling constants. The values shown in Table 1 were obtained using eq 4 at 320 K and at an

magnetic moments at individual sites averaged over all Monte Carlo iterations. They were evaluated at each temperature step as

Φi(T ) =

⟨MMC(T )⟩i Msat

(4)

where ⟨MMC(T)⟩i is the average magnetic moment for Mni-type sites.

3. RESULTS AND DISCUSSION 3.1. 23Na NMR of Stoichiometric β-NaMnO2. 3.1.1. Planar Defects Revealed by Experimental 23Na NMR. Asprepared β-NaMnO2 contains structural defects such as twin boundaries between local domains of orthorhombic (β) and monoclinic (α) symmetry.7,11 The 23Na NMR spectrum of the as-synthesized β-NaMnO2 compound acquired at a magnetic field strength of 4.7 T (Figure 3a; adapted from Billaud et al.7)

Figure 3. Room temperature spin echo 23Na NMR spectra collected at 60 kHz magic angle spinning (MAS) and at B0 = 4.7 T on (a) the β-NaMnO2 cathode material as-synthesized and after five electrochemical (charge/discharge) cycles, and on (b) α-NaMnO2. The peaks corresponding to Na nuclei in α-like, β-like environments, and in the vicinity of a twin boundary are denoted as Naα, Naβ, and NaSF, respectively. Both α- and β-NaMnO2 samples contain twin planes, as demonstrated by the NaSF resonance present in the spectra. NMR parameters obtained from fits of the data are shown on the spectra. Spinning sidebands due to fast MAS are indicated by (*). The peak near 0 ppm in (a) is due to Na+ in a diamagnetic environment, most probably from residual electrolyte or its decomposition products formed during cycling. Figures adapted with permission from ref 7. Copyright 2014 American Chemical Society.

Table 1. Site-Specific Scaling Factors Φα, Φβ, and ΦSF Obtained from Monte Carlo Simulations and the Bulk Scaling Factor Obtained from the Experimental Magnetic Susceptibilitya Monte Carlo

confirms the presence of multiple Na sites. Based on this work7 and a preliminary study,43 the two main resonances with isotropic shifts δiso = 318 and 528 ppm were assigned to Na in an ideal “β-like” environment (Naβ) and to Na in the vicinity of a twin boundary (NaSF), respectively. This assignment is corroborated by the NMR data collected on the same sample at a much higher field of 23.5 T shown in Figure S5 in the SI. The third, very low intensity peak with an isotropic shift δiso = 751 ppm matches the Na resonance observed in the spectrum of the α polymorph (see Figure 3b) and was assigned to Na in an “α-like” local environment (Naα) within the stacking faults in the β-NaMnO2 phase.7 Integration of the three resonances observed in the spectrum of as-synthesized β-NaMnO2 indicates that about 65.5% of Na nuclei are in β-like environments, 32% are in the vicinity of a twin boundary, and 2.5% are in α-like environments. We discuss the nature of these faults in section 3.3.3. The results are in good agreement with our previous work which showed that the broadening of the (011) peak in the XRD pattern of the β-NaMnO2 compound could be simulated if stacking faults were randomly introduced into 25% of the layers in the

Φα Φβ ΦSF exptl (bulk)

EXP H20 9.87 7.91 8.90 6.64

× × × ×

10−3 10−3 10−3 10−3

EXP H35

OPT H20

OPT H35

1.19 × 10−2 1.02 × 10−2 1.10 × 10−2

9.12 × 10−3 6.96 × 10−3 8.07 × 10−3

1.13 × 10−2 9.21 × 10−3 1.03 × 10−2

a

MPMS data are shown in Figure S3 in the SI. All values reported here were derived at 320 K and at 4.7 T. The site-specific scaling factors were obtained from simulations performed on Mixed Cell 1 (see Figure 2a), using magnetic exchange couplings obtained from the experimental (EXP) and first-principles optimized (OPT) α- and β-NaMnO2 structures using the H20 and H35 functionals (see Table S2 in the SI).

external field of 4.7 T. We note that very similar scaling factors were obtained for the two Mn sites at the interfaces between the α- and β-like domains, in environments similar to the Na(1) and Na(2) sites in Figure 2, so that an average ΦSF scaling factor is used for both Mn interfacial sites hereafter. The site-specific scaling factors shown above are systematically overestimated in comparison with the experimental bulk scaling factor. Possible reasons for this result are the lack of diamagnetic contributions, demagnetizing fields, magneto-elastic 8231


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Chemistry of Materials coupling, spin−orbit effects (probably small, since a g-value of 1.993 has been reported for α-NaMnO244), spin canting, and uniaxial magnetic anisotropy (reported for α-NaMnO244,45) in the Monte Carlo simulations. To account for the differences between the experimental and simulated results, we have adopted a pragmatic approach and have simply rescaled the Monte Carlo scaling factors by a factor k so as to reproduce the experimental bulk scaling factor at this temperature: Φ(320 K) = k(Φα fα + Φβ fβ + ΦSF fSF )

information about the magnetic properties of the different paramagnetic species contributing to the total Na shift to be retained. First-Principles 23Na NMR Parameters on the α- and β-NaMnO2 Structures. First-principles NMR parameters for α- and β-NaMnO2 are recorded in Table 3. The structures obtained following optimization are more contracted than the experimental structures, leading to greater orbital overlap, a larger delocalization of electronic density and larger hyperfine shifts. A previous theoretical study on a selection of cubic perovskites showed that an increase in the percentage of Fock exchange in the hybrid DFT/HF functional leads to a more compact structure.46 A similar trend is observed here for the relaxed α- and β-NaMnO2 structures obtained using 20 and 35% Fock exchange, as shown in Table S1 in the SI. Focusing on the OPT results, the isotropic shift of Na in an α- and β-like environment are expected to be in the ranges of 676−1109 and 181−388 ppm, respectively. These ranges of shifts (and those obtained for the EXP structures) are consistent with the experimental isotropic shifts of 751 and 318 ppm for Naα and Naβ, respectively (see Figure 3). Considering the strong dependence of the calculated quadrupolar and hyperfine NMR parameters on the structure (OPT vs EXP) and local geometry around the 23Na nuclei, our first-principles results on the α- and β-NaMnO2 phases agree well with the experimental data shown in Figure 3, and with a recent variable-temperature 23Na NMR study on α-NaMnO2, where parameters ηQ = 0.54, CQ = 3.03 MHz, and δiso = 707 ppm were obtained for the main Na site at 300 K.10 In the same work, a value of 950 ppm was reported for the principal component of the anisotropic part of the hyperfine interaction tensor, δZZ, responsible for the line shape of the 23Na NMR central transition.10 Our calculations in the OPT α-NaMnO2 structure predict that δZZ = 1090−1139 ppm for the lower temperature of 300 K, with limits set by the H20 and H35 results. NMR Signature of Na Local Environments near Planar Defects. First-principles 23Na NMR parameters for the different environments in the Mixed Cell 1 and Mixed Cell 2 structures, depicted in Figure 4, are presented in Table 4. Na(1) and Na(2) sites, shown in Figure 4a,b, feature the same number and type of Mn−O−Na interactions and differ only in the spatial arrangement of the atoms around the central Na, leading to similar Fermi contact shifts yet different hyperfine dipolar and quadrupolar NMR parameters (Table 4a). Since the Fermi contact shift is much larger than the second

(5)

where fα, fβ, and f SF are the fractions of Mn spins in α-like and β-like nanodomains, and those close to a twin boundary in the β-NaMnO2 sample under study, respectively, quantified from the intensities extracted from the 23Na spectrum: fα = 0.025, fβ = 0.655, and f SF = 0.32. The final site-specific scaling factors for the four different simulations, Φ′i = k Φi

(6)

are presented in Table 2. Table 2. Site-Specific Scaling Factors Φα′ , Φβ′ , and ΦSF ′ at 320 K, Computed Using Eqs 5 and 6a

Φα′ Φβ′ Φ′SF

EXP H20 (k = 0.89956)

EXP H35 (k = 0.68494)

OPT H20 (k = 0.80225)

OPT H35 (k = 0.63756)

7.92 × 10−3 6.34 × 10−3 7.14 × 10−3

7.56 × 10−3 6.48 × 10−3 6.94 × 10−3

8.21 × 10−3 6.26 × 10−3 7.26 × 10−3

7.73 × 10−3 6.37 × 10−3 7.05 × 10−3

a

EXP/OPT and H20/H35 correspond to the scaling factors obtained from Monte Carlo results using sets of coupling constants computed in the experimental (EXP) and first-principles optimized structures (OPT), and using the H20 and H35 exchange-correlation functionals.

OPT (EXP) H20 (H35) scaling factors were used to scale the OPT (EXP) H20 (H35) first-principles 23Na NMR shifts presented in Tables 3 and 4. This is the first time that site-specific scaling factors are used to compare first-principles NMR parameters to experimental data. The importance of this approach in materials containing inequivalent NMR sites and/ or structural domains is illustrated by the consistent differences shown in the sizes of the site-specific scaling factors in Table 2, Φ′α > Φ′SF > Φ′β. In systems containing a mixture of metal ion types, the combination of site-specific scaling factors and pathway decomposition analysis (introduced later) allows local

Table 3. First-Principles 23Na NMR Parameters Obtained Using H20 and H35 Hybrid Functionals, and Using Either the Experimental (EXP) or First-Principles Optimized (OPT) α-NaMnO2 and β-NaMnO2 Structuresa α-NaMnO2 (751 ppm/|3.03| MHz)

β-NaMnO2 (318 ppm/|2.61| MHz)

parameter

EXP H20

EXP H35

OPT H20

OPT H35

EXP H20

EXP H35

OPT H20

OPT H35

δiso/ppm Δδ/ppm η CQ/MHz ηQ δQ/ppm δiso + δQIS/ppm

978 1563 0.19 −3.56 0.24 −115 864

567 1498 0.17 −3.60 0.26 −118 449

1109 1709 0.19 −2.39 0.81 −62 1047

676 1635 0.17 −2.46 0.69 −63 613

272 764 0.78 2.53 0.86 −71 201

61 788 0.75 2.56 0.84 −72 −11

388 845 0.67 2.85 0.55 −80 309

181 878 0.63 3.04 0.38 −86 95

a In this table and in Table 4, the isotropic shift (δiso, in ppm), dipolar anisotropy (Δδ= δzz − 1/2(δxx + δyy), in ppm), dipolar asymmetry (η), quadrupolar coupling constant (CQ, in MHz), quadrupolar asymmetry (ηQ), second-order induced quadrupolar shift (δQIS, in ppm), and net shift (δiso + δQ, in ppm) are calculated for a temperature of 320 K and B0 = 4.7 T. The experimental structures of α-NaMnO2 and β-NaMnO2 are shown in Figure 1,2,9 and the scaling factors Φ′α and Φ′β used to scale the Na(α) and Na(β) shifts, respectively, are given in Table 2. The experimental isotropic shift and CQ values (Figure 3) are given in parentheses in the top headings.

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line width of the Na resonances. It would therefore be difficult, in practice, to distinguish the two sites in the experimental NMR spectrum. The hyperfine shifts computed for Na(α) (Table 3 and Figure 4e) and Na pseudo-α sites (Table 4b and Figure 4c) (and for Na(β) (Table 3 and Figure 4f) and Na pseudo-β sites (Table 4b and Figure 4d)) are alike for reasons similar to those outlined above. While for the Na(β), Na(1), and Na(pseudo-α) environments, the four Mn ions in the P2 position are either all below or all above the horizontal plane containing the central Na (see Figure 4), for Na(α), Na(2), and Na(pseudo-β) sites there are two Mn ions in P2 position on either side of the horizontal plane. This is consistent with the first-principles results (see Tables 3 and 4), which reveal a small electron−nuclear dipolar asymmetry parameter (η), comprised between 0.05 and 0.18, for the latter type of environments, and a larger η parameter, comprised between 0.60 and 0.98, for the former, less symmetrical environments. Pathway Decomposition Analysis of the 23Na NMR Shifts. The total 23Na Fermi contact shift may be decomposed into individual Mn−O−Na bond pathway contributions (BPCs), Pi (Figure 5), providing a rationale for the very different shifts observed for the various Na site types in the NaMnO2 material. The BPCs were evaluated from the variations in the spin density at the Na nucleus after selected Mn spin flips in 32 formula unit supercells of α- and β-NaMnO2, the difference in spin density at the 23Na nucleus in the totally ferromagnetic case and after an individual spin flip being proportional to the 23Na contact shift induced by the flipped Mn spin.20 The pathway contributions in the α and β forms are very similar, save that pathways P1 and P3 in α-NaMnO2 are split into two inequivalent but similar pathways labeled P1a and P1b, and P3a and P3b, respectively, in β-NaMnO2. The major difference between the hyperfine parameters of the two polymorphs of NaMnO2 may be largely attributed to the lack of a P4-type (approximately 180°) interaction in β-NaMnO2,

Figure 4. Na local environments present in the various NaMnO2-type structures shown in Figure 2: (a) Na(1) and (b) Na(2) sites in the Mixed Cell 1 structure, (c) Na(pseudo-α) and (d) Na(pseudo-β) sites in the Mixed Cell 2 structure, (e) Na(α) site in α-NaMnO2, and (f) Na(β) site in β-NaMnO2.

order quadrupolar shift, the total shifts of Na(1) and Na(2) differ by less than 50 ppm, which is smaller than the inherent

Table 4. First-Principles 23Na NMR Parameters Obtained Using H20 and H35 Hybrid Functionals on the (a) Mixed Cell 1 and (b) Mixed Cell 2 Structures Shown in Figure 2a,ba (a) Mixed Cell 1 Na(β) (318 ppm/|2.61| MHz)

Na(1) (528 ppm/|2.80| MHz)

parameter

H20

H35

H20

δiso/ppm Δδ/ppm η CQ/MHz ηQ δQ/ppm δiso+δQ/ppm

379 845 0.67 2.80 0.56 −77 302

169 878 0.63 2.95 0.41 −82 87

704 −852 0.98 2.70 0.70 −75 628

H35 404 841 0.96 2.77 0.64 −78 326 (b) Mixed Cell 2

Na(2) (528 ppm/|2.80| MHz)

Na(α) (751 ppm/|3.03| MHz)

H20

H35

H20

H35

776 1504 0.13 −2.77 0.99 −90 686

469 1486 0.10 −2.83 1.00 −95 373

1179 1689 0.18 −2.81 0.87 −88 1091

750 1615 0.16 −2.89 0.83 −91 658

Na(pseudo-α)

Na(pseudo-β)

parameter

H20

H35

H20

H35

δiso/ppm Δδ/ppm η CQ/MHz ηQ δQ/ppm δiso + δQ/ppm

1097 −999 0.60 2.60 0.85 −75 1022

640 −925 0.67 2.60 0.85 −75 565

441 1315 0.07 2.85 0.92 −93 348

199 1346 0.05 2.88 0.89 −93 106

a The different types of Na environments present in the structures are shown in Figure 4. Φα′ , Φβ′ , and ΦSF ′ (Table 2) were used to scale the total Na(α)/Na(pseudo-α), Na(β)/Na(pseudo-β), and Na(1)/Na(2) isotropic shifts, respectively. The experimental isotropic shifts and CQ values (Figure 3) are given in parentheses in the top headings.

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Table 5. Energy Differences between the Monoclinic (α) and Orthorhombic (β) Forms of NaMnO2, Eα − Eβ, Computed for Ferromagnetic and Antiferromagnetic Alignmentsa Eα − Eβ source

method

compound

FO

AFM

Velikokhatnyi et al.48 Abakumov et al.11

GGA GGA + U (Ueff = 2 eV) GGA + U (Ueff = 3.9 eV)

NaMnO2 NaMnO2

−16 −10

−11 18

NaMnO2

−12

5

this work

EAFM − EFO (β) −152 not calculated −51

a

All values are indicated in meV per formula unit. The results obtained in this study with a U parameter of 3.9 eV are compared with prior results obtained with no48 or a smaller11 U value.

NaxMnO2,39 predicting that the AFM ground state formation energies of the α and β forms of NaMnO2 differ by only 5 meV per formula unit. This energy difference falls in between the two values reported previously.11,48 The results shown here suggest that AFM β-NaMnO2 is slightly favored at 0 K. As mentioned earlier, the α form is the thermodynamically stable form at room temperature,2 which may arise from entropic effects, temperature-dependent Jahn−Teller effects, and/or the weaker magnetic interactions of the two forms at the temperatures at which these compounds are made. The results, however, suggest that the total Gibbs free energy difference between α- and β-NaMnO2 at 25 °C may also be small enough that a phase mixture is likely in any NaMnO2 sample at room temperature, if the interfacial energies between domains are sufficiently low. We note that the kinetics of stacking fault formation during sample preparation (at high temperatures) will also affect the concentration and nature of the defects. Additional insight into the driving force for the formation of stacking faults in NaMnO2 can be gained from a comparison of the formation energies of the ideal α- and β-NaMnO2 structures, with that of Mixed Cell 1 containing twin planes separating α and β nanodomains. GGA+U computations on ferromagnetically aligned cells show that Mixed Cell 1, composed of two-fifths of α-type and three-fifths of β-type layer stacking, is about ΔE = 0.7 meV per formula unit lower in energy than the appropriate weighted sum of the energies of the α and β domains (obtained from the energies of the ideal α- and β-NaMnO2 structures). This corresponds to a negative interfacial energy, Eint = −0.2 meV/A2 (−0.003 J/m2), between α and β structural domains, suggesting that the creation of twin planes is energetically favored. The interfacial energy computed here should be interpreted in qualitative rather than quantitative terms, since no account is taken of contributions from long-range structural strain or magnetism. In addition, these calculations are performed with periodic boundary conditions and may not give an accurate description of the interfacial energy at the surface of the particles, which will clearly also depend on particle size. Parameterizing the strain would require the computation of ΔE for a series of mixed cells of differing lengths in the direction perpendicular to the interface, which is beyond the scope of this work. Nevertheless, the results presented here demonstrate that the interfacial energy between α- and β-NaMnO2 is about 2−3 orders of magnitude smaller than typical surface energies (0.1−3 J/m2) and explains the strong propensity for structural intergrowths between the two forms. 3.3. 23Na NMR Investigation of the Na Deintercalation Mechanism and of the Evolution of the β-NaMnO2 Structure with Electrochemical Cycling. 3.3.1. Evolution

Figure 5. Mn−O−Na hyperfine interaction pathways and shift contributions (Pi) in (a) α-NaMnO2 and (b) β-NaMnO2. Mn−O− Na bond pathway contributions (BPCs) were calculated with firstprinciples optimized (OPT) structures, and those in brackets with the experimental structures of Parant et al.2 and Hoppe et al.9 using the H20 and H35 functionals. The scaling factors Φ′α and Φ′β used to scale the BPCs are given in Table 2. Note that the P1 and P2 bond pathway contributions both correspond to two 90° Na+−O−Mn3+ interactions.

leading to a much smaller overall shift. An analysis of the different orbital interactions leading to the various Pi contributions in α-NaMnO2 (Figure S4), and a description of the bond pathway geometries in the two polymorphs (Table S4a,b), is presented in the SI. Summing the contributions (multiplied by their degeneracies) results in a total isotropic shift between 672 and 1062 ppm (H35 and H20) for α-NaMnO2, and between 206 and 397 ppm (H35 and H20) for β-NaMnO2, in the OPT structures. These shifts are in good agreement with the isotropic shifts computed on the primitive cells presented in Table 3, supporting the pairwise BPC model of the shifts presented here. The bond pathway analysis clearly demonstrates that the two additional P4 interactions (see Figure 5) are responsible for the larger overall Na(α) and Na(pseudo-α) shifts, compared to those of Na(β) and Na(pseudo-β) sites. The presence of a single P4 Mn−O−Na interaction pathway for Na(1) and Na(2) sites in the vicinity of a planar defect in NaMnO2 gives rise to a total shift intermediate between that of Na(α) and Na(β). 3.2. Why Are There Stacking Faults in NaMnO2? The total energies of α- and β-NaMnO2 were computed, and both ferromagnetic (FO) and AFM spin alignments were investigated and compared with those of others (Table 5). All AFM results reported here (for the α and β structures) used the AF3 AFM alignment proposed by Singh et al.47 for α-LiMnO2 (the Li analogue of α-NaMnO2); this alignment is consistent with the exchange coupling constants (Ja) obtained for α- and β-NaMnO2 presented in Table S2 in the SI. As shown in Table 5, the ground state energy difference between α- and β-NaMnO2 is small irrespective of the spin alignment. When it comes to computing the formation energies and the (de)intercalation voltages of strongly correlated materials, such as transition metal oxides, GGA+U generally yields more accurate results than pure GGA.38 Here, a Ueff Hubbard parameter of 3.9 eV was used for Mn in line with previous work on 8234


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Chemistry of Materials of the 23Na NMR of β-NaxMnO2 during the First Electrochemical Cycle. Building upon our previous work,7 the structural rearrangements occurring upon Na (de)intercalation from β-NaxMnO2 are monitored by fitting the 23Na NMR spectra collected at different points along the first cycle, as shown in Figure 6. The NMR lineshapes are significantly broadened

Figure 7. Site occupancies, for the various Na environments observed at different points along the first electrochemical cycle of the β-NaxMnO2 cathode, as obtained from fits of the 23Na NMR data presented in Figure 6. Error bars represent the standard deviation in the peak area obtained from multiple fits of the data. The environments with a 0 ppm shift correspond to diamagnetic Na in residual electrolyte or in its decomposition products formed upon cycling. LRO and SRO correspond to long- and short-range order, respectively.

x = 0.51 material, suggesting that the structural changes lag the electrochemical changes and that the two-phase reaction is kinetically sluggish. Common features are observed in the 23Na NMR spectra collected on samples with a Na content between 0.56 and 0.38. In this range, Na site occupancies evolve in a complex manner, presumably due to a variety of structural rearrangements occurring in the material. A peak with an isotropic shift of about 1000 ppm appears in the spectra and is more clearly visible at x = 0.43 and 0.38 (Figure 7). The presence of two broad resonances at 700 and 1000 ppm suggests the coexistence of various local environments/phases with different Na contents. The two “pristine peaks” at 318 and 528 ppm are observed up to ca. 3.6 V (x = 0.38), which demonstrates that a significant proportion of the remaining Na occupies local environments similar to those found in the stoichiometric β-NaMnO2 phase, albeit subject to local structural distortions (e.g., induced by lattice parameter changes upon Na extraction) leading to peak broadening. In situ powder XRD data indicated the loss of long-range order at low Na contents, while TEM data revealed a mosaic structure of crystal domains in the end-of-charge material.7 The spectra obtained for the high voltage NaxMnO2 samples (x < 0.38) contain two very broad peaks centered at approximately 700 and 1000 ppm, which are indicative of short-range disorder and of the formation of a large number of Na environments.7 As discussed in our previous paper7 and shown in Figures 6 and 7, the initial long-range and local crystal structures are recovered upon discharge. 3.3.2. From Which Sites Are Na+ Ions First Extracted? The faster decrease in the intensity of the Naβ NMR signal at the beginning of charge (x ≥ 0.51) as compared with the NaSF signal was discussed in our previous work7 and is clearly shown in Figure 7. Because a two-phase reaction is taking place between NaMnO2 and Na∼0.57MnO2 over this voltage range, relative NaSF:Naβ site occupancy must be larger in the new Na∼0.57MnO2 phase than in the as-prepared material. As mentioned previously,7 this may result from a variety of different phenomena: the growing phase exhibits a greater number of stacking faults than

Figure 6. Room-temperature spin echo 23Na NMR spectra obtained under 60 kHz MAS and at B0 = 4.7 T on various NaxMnO2 samples stopped at different points along the first electrochemical charge and discharge of β-NaMnO2. The spectra have been normalized according to the number of scans and to the amount of active material in the NMR rotor. The electrochemical profile (voltage vs Na content) is shown on the left. The filled circles indicate the Na content at which each spectrum on the right was obtained. The 0 ppm peak corresponds to diamagnetic Na environments originating from residual electrolyte or its decomposition products formed upon cycling. Adapted with permission from ref 7. Copyright 2014 American Chemical Society.

by the strong paramagnetic interactions in NaxMnO2 (x < 0.8) phases, and by the distribution of local environments in the material, hampering the extraction of unambiguous quadrupolar NMR parameters. The area under each of the fitted peaks, corresponding to the occupation number of a particular Na site type, is plotted as a function of Na content in Figure 7. The evolution upon charge of the site occupancies of the different Na environments in β-NaxMnO2 falls into three broad regimes: (i) Na content x > 0.51, (ii) x = 0.51−0.38, and (iii) x < 0.38. The trends observed upon charge are clearly reversed upon discharge. At the beginning of charge, the “Naβ” and “NaSF” peaks observed in the pristine β-NaMnO2 NMR spectrum (see Figure 3a) gradually diminish, while a peak at about 700 ppm appears and increases (Figure 7). This is consistent with the two-phase reaction between NaMnO2 and Na∼0.57MnO2 observed with in situ powder XRD giving rise to extended electrochemical plateaus at 2.6−2.7 V vs Na+/Na(s) upon charge and subsequent discharge, as shown in our previous study.7 While the electrochemical curve suggests that the two-phase region ends at x = 0.57 upon charge, the NMR data reveal that the pristine NaMnO2 phase is still present in the 8235


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Chemistry of Materials the as-synthesized phase, Na+ ions are more easily extracted from the Naβ sites so that more Na are found in NaSF sites in the growing phase, and/or a new resonance with the same shift of that of the NaSF is formed. Further insight into the energetics of Na (de)intercalation from all Na sites in the material can be obtained from redox potential calculations in the Mixed Cell 1 and end-member α- and β-NaMnO2 structures. Na (de)intercalation potentials are evaluated from total energies via the methods of Ceder and co-workers.38,49 The average cell potential for Na insertion between two composition limitsNaMnO2 and Na1−xMnO2is determined by computing the total energies, E, of NaMnO2, Na1−xMnO2, and Na(s): ⟨V ⟩ =

Hence, preferential oxidation of Mn in P3 and P4 position to a vacant Na site, as evidenced by Na deintercalation potential calculations, is consistent with the higher average Na shift observed for the Na∼0.57MnO2 phase formed upon initial charge of the disordered β-NaMnO2 cathode (see Figure 6). Previous studies on AxMO2 (A = Li, Na; M = Ni, Mn) compounds have shown that in layered oxides containing a trivalent Jahn−Teller metal species, the formation of energetically favorable 180° A-O-M3+-O-A interactions along the Jahn− Teller elongated bonds leads to a strong coupling between M3+/M4+ charge and orbital ordering, and alkali ion/vacancy ordering.39,50−52 The creation of an alkali vacancy □ along the Jahn−Teller bond of the M3+ cation is disfavored. In α-NaMnO2, the number of unfavorable 180° □-O-M3+-O-A interactions is minimized when the +4 Mn oxidation state localizes in the P4 position relative to the vacant Na(α) site. In this case, a 180° □-O-M4+-O-A interaction is formed (the empty dz2 orbital on the Mn4+ site pointing directly to the vacant site) and the cooperative Jahn−Teller elongation in this direction is effectively broken. There are no P4 Mn positions relative to a vacant Na(β) site, which is why the +4 charge localizes onto a Mn in position P3 (see Figure 5) i.e., at the extension of a 180° □-O-M interaction but not along the Jahn−Teller axis of the cell. For a vacant Na site in the vicinity of a stacking fault, calculations performed for Na(1) and Na(2) in Table 6 demonstrate that it is almost equivalent to localize the +4 state onto a Mn site in the P3 or P4 position relative to the Na vacancy (with a slight preference for the P3 position), which is again consistent with the higher average Na shift observed for the Na∼0.57MnO2 phase. The different Na sites in Mixed Cell 1, arranged in order of increasing (de)intercalation potential, are Na(α) (2.56 V) < Na(β) (2.66 V) < Na(2) (2.67−2.72 V) < Na(1) (2.75− 2.80 V). These potentials are consistent with the more rapid decrease of the Naβ signal, as compared with NaSF, observed in the 23Na NMR data at the beginning of charge, the Naα signal being too weak to be observed upon charge. Note that the calculations above describe the first stages of Na deintercalation and do not necessarily reflect the Na configurations or sites that are removed on forming Na0.57MnO2. Interestingly, the average Na (de)intercalation potential computed for Na(α) sites in Mixed Cell 1 is 0.14 V lower than the average potential obtained for α-NaMnO2. The higher deintercalation potential computed in the ideal α-NaMnO2 structure is likely related to the oxidation of Mn along the Jahn−Teller axis (P4 to the vacancy), i.e., to the disruption of orbital order, or to the structural strain associated with the disruption of the cooperative Jahn−Teller distortion.39,48 The presence of stacking faults in Mixed Cell 1 decreases the energy of the final state (i.e., after Na extraction). This effect is not observed upon Na removal from Na(β) sites (a potential difference of only 0.04 V is found between Mixed Cell 1 and β-NaMnO2), since Mn is oxidized in position P3 and does not affect the cooperative Jahn−Teller distortion nor orbital ordering to as great an extent as in α-NaMnO2. The first-principles redox potentials reported here are in excellent agreement with previous experimental studies. Using the potentiostatic intermittent titration technique (PITT), Ma et al. observed a first oxidation process at 2.59 V for α-NaMnO2,6 in good agreement with the initial Na (de)intercalation potentials obtained for Na(α) in Mixed Cell 1 (2.56 V) and in α-NaMnO2 (2.66 V). GITT (galvanostatic intermittent titration technique) measurements for β-NaMnO2 showed that the equilibrium potential at the beginning of charge is 2.65 V,7

−[E(NaMnO2 ) − E(Na1 − xMnO2 ) − xE(Na(s))] xF (7)

where x is the fraction of Na removed from/inserted into the cell and F is the Faraday constant. The average potentials presented in Table 6 correspond to the (de)intercalation of Table 6. Average (De)intercalation Potentials ⟨V⟩ Obtained for the Different Na sites in Mixed Cell 1 and in the EndMember α- and β-NaMnO2 Structuresa structure

Na site

⟨V⟩/V

Mixed Cell 1

Na(1) Na(1) Na(2) Na(2) Na(2) Na(α) Na(β) Na(α) Na(α) Na(β) Na(β)

2.80 2.75 2.72 2.67 2.87 2.56 2.66 2.69 2.82 2.64 2.89

α-NaMnO2 β-NaMnO2

charge localization localized on localized on localized on localized on delocalized localized on localized on localized on delocalized localized on delocalized

Mn Mn Mn Mn

in in in in

P4 P3 P4 P3

Mn in P4 Mn in P3 Mn in P4 Mn in P3

a

The site on which the electron hole (forming a Mn4+ ion) localizes upon Na extraction is specified in the column on the right. P3 and P4 refer to the same Mn positions as shown in Figure 5 for the Na environments in α- and in β-NaMnO2.

one Na atom in a 40 formula unit supercell (1 Na in 40 is (de)intercalated), i.e., between compositions NaMnO2 and Na0.975MnO2. The average Na (de)intercalation potential computed for the different Na sites depends upon the extent to which the charge created upon removal of one Na+ ion delocalizes. Charge localization onto one Mn site in the first coordination shell around the Na vacancy leads to an average potential 0.13 to 0.26 V lower than that computed when the charge is delocalized over a number of Mn sites (for α- and β-NaMnO2, respectively). In fact, when a Na vacancy is created on a Na(α) (Na(β)) site in Mixed Cell 1, the 4+ charge localizes spontaneously onto a Mn in P4 (P3) position with respect to the vacant site, using the same pathway notation as given in Figure 5. First-principles calculations of Mn4+ BPCs in partially desodiated α- and β-NaxMnO2 (x < 1) structures suggest a net reduction (increase) in the total Na shift upon Mn oxidation in P3 and P4 (P1 and P2) position to a Na ion. The P2 and P4 BPCs (with respect to a Na ion) are particularly affected upon Mn oxidation, presumably because these pathways proceed via Jahn−Teller elongated Mn−O bonds in the stoichiometric NaMnO2 phases. 8236


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4. CONCLUSIONS A detailed solid-state 23Na NMR and first-principles DFT study of the evolution of the structure of the β-NaMnO2 cathode material was undertaken. It was found that the as-synthesized β-NaMnO2 phase contains a number of planar defects identified as twin planes between nanodomains of the α- and β-NaMnO2 polymorphs, in agreement with previous reports.7,11 This result was corroborated by GGA+U calculations revealing that the total energies of the two polymorphs of NaMnO2 are within 5 meV per formula unit, well below the Boltzmann energy at room temperature and suggesting facile intergrowth between the α and β structures. 23Na NMR data acquired at different points along the first electrochemical cycle confirmed the presence of a two-phase reaction at the beginning of charge and at the end of discharge, consistent with the plateaus at 2.6−2.7 V in the voltage vs capacity plot. GGA+U computations of Na (de)intercalation potentials revealed that, at the beginning of charge, Na ions are extracted preferentially from α-like nanodomains, then β-like regions, and finally from sites near the twin planes, in good agreement with the experimental NMR data. 23 Na NMR indicated that 65.5% and 59% of the Na+ ions are in β-NaMnO2 domains in the as-synthesized material, and after five electrochemical cycles, respectively. On the other hand, the ratio of α-NaMnO2-type Na sites increases from 2.5 to 11% over the first five cycles, while the number of Na+ ions near a twin plane between α- and β-NaMnO2 domains is relatively constant, between 32 and 30%. More Na in α-NaMnO2-type Na sites after five cycles suggests that, upon extended cycling, twin boundaries separate the major β-NaMnO2 phase from larger α-NaMnO2 domains.

in very good agreement with the potentials calculated for Na(β) sites in Mixed Cell 1 (2.69 V) and in β-NaMnO2 (2.64 V). 3.3.3. Structural Changes in the β-NaMnO2 Cathode after Multiple Cycles. The first-principles 23Na NMR parameters presented in Tables 3 and 4 indicate that the Naα (Naβ) experimental peaks have contributions from Na nuclei in α-like (β-like) and pseudo-α (pseudo-β) environments. The NaSF peak has contributions from Na nuclei in Na(1) and Na(2) sites (Mixed Cell 1, Figure 2a) with Na−O−Mn pathways intermediate between those found for the Na sites in α- and β-NaMnO2. These findings, and the relative occupation of the different Na environments revealed by experimental NMR, allow us to consider particular types of planar defects present in as-synthesized β-NaMnO2 and in the material after five electrochemical cycles. The stacking fault shown in Mixed Cell 1 contains a ratio between Na sites in α-NaMnO2 domains and in the vicinity of a twin boundary that must always be greater than two; this is not consistent with experiment and thus different stacking fault sequences must also be present. Structural models based on Mixed Cell 2-type faults would result in more α-like environments than observed experimentally, hence the two possible stacking sequences considered here are closer to the Mixed Cell 1 scheme, as shown below. The proportion of Naβ, NaSF, and Naα sites in the structure shown in Figure 8a is 66.7, 30.8, and 2.6%, respectively, very

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.6b03074. Additional computational details; NaMnO2-type structures considered in this work; first-principles magnetic coupling constants; evaluation of bulk and site-specific magnetic scaling factors; bond pathway decomposition analysis in α- and β-NaMnO2; additional experimental details (23Na NMR) and complementary 23Na NMR data at a 1 GHz external field (PDF)

■ ■

AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was partially supported by the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Vehicle Technologies, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231, under the Batteries for Advanced Transportation Technologies (BATT) Program subcontract no. 7057154 (R.J.C). C.P.G. and R.J.C. thank the EU ERC for an Advanced Fellowship for C.P.G. Via our membership in the UK’s HEC Materials Chemistry Consortium, funded by EPSRC (EP/L000202), the first-principles calculations presented in this work used the ARCHER UK National Supercomputing Service (http://www.archer.ac.uk). Calculations were also carried out in part at the Center for Functional Nanomaterials, Brookhaven National Laboratory, which is supported by the U.S. Department of Energy, Office of

Figure 8. Possible stacking sequences observed in (a) as-synthesized β-NaMnO2 and (b) β-NaMnO2 after five electrochemical cycles based on the observed integrated intensities of the experimental Naα, Naβ, and NaSF NMR peaks.

close to the distribution of Na site types in the as-synthesized β-NaMnO2 sample studied earlier. The proportion of Naβ, NaSF, and Naα sites in the structure shown in Figure 8b is 57.9, 31.6, and 10.5%, respectively, similar to the distribution of Na site types in the β-NaMnO2 sample obtained after five cycles. A higher fraction of α-NaMnO2 domains, or Na in these domains, is observed after cycling, suggesting that structural rearrangements occur, leading to twin boundaries separating larger α-NaMnO 2 domains from the major β-NaMnO 2 phase. 8237


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Basic Energy Sciences, under Contract No. DE-SC0012704. Rob Armstrong, Peter Bruce, and Juliette Billaud are thanked for helpful discussions and for providing the samples studied by NMR. Richard Harrison is thanked for help with the implementation of the Monte Carlo code in Python. Kellie Aldi and Jordi Cabana are acknowledged for their participation in a preliminary study on NaMnO2. Hajime Shinohara and Sian Dutton are thanked for their help with the experimental susceptibility measurements. Rebecca Dally and Steven Wilson are thanked for providing the samples for the high-temperature experimental magnetic susceptibility measurements.

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Insights into the Nature and Evolution upon Electrochemical Cycling of

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