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Rationalization of Intercalation Potential and Redox Mechanism for A2Ti3O7 (A = Li, Na) Gwenaelle Rousse,†,‡,§ M. Elena Arroyo-de Dompablo,*,⊥ Premkumar Senguttuvan,∥,#,⊗ Alexandre Ponrouch,∥,⊗ Jean-Marie Tarascon,‡,§,#,⊗ and M. Rosa Palacín*,∥,⊗ †

Institut de Minéralogie et de Physique des Milieux Condensés (IMPMC) UMR 7590, CNRS−Université Pierre et Marie Curie UPMC (University of Paris 06), Case courrier 115, 4 Place Jussieu, 75252 Paris Cedex 05, France ‡ Collège de France, 11 place Marcelin Berthelot, 75231 Paris Cedex 05, France § Réseau sur le Stockage Electrochimique de l’Energie (RS2E), CNRS FR3459, 80039 Amiens, France ⊥ Departamento de Química Inorgánica, Universidad Complutense de Madrid, 28040 Madrid, Spain ∥ Institut de Ciència de Materials de Barcelona (ICMAB-CSIC) Campus UAB, E-08193 Bellaterra, Catalonia, Spain # Laboratoire de Réactivité et Chimie des Solides, UPJV, CNRS UMR 7314, 33 rue Saint Leu, 80039 Amiens, France ⊗ ALISTORE ERI European Research Institute, 33 Rue Saint Leu, 80039 Amiens, France S Supporting Information *

ABSTRACT: Na2 Ti3O 7 was recently reported to be highly promising as a negative electrode material for Na-ion batteries, thanks to its very low intercalation voltage (0.3 V vs Na+/Na0) and high capacity (200 mAh/g). The investigation of the redox mechanism in A2Ti3O7 (A = Li, Na) upon additional alkali ion intercalation concomitant to reduction of titanium is reported in this paper. Even if the low stability of the reduced phases (A2+xTi3O7) precluded a direct study, density functional theory (DFT) calculations allowed us to propose structural models for the reduced phases (A2+xTi3O7), which were further successfully confronted to the available experimental data. The alkali atoms are octahedrally coordinated in the reduced A2+xTi3O7 phase, so that the whole resulting structure can be considered rocksalt type. The very different potentials at which ion insertion is observed for A = Li or A = Na clearly prove that analogies between lithium and sodium systems cannot be taken for granted. In this case, such findings can be fully rationalized through DFT and arise from the differences in polarizing character between lithium and sodium ions that cause, respectively, contraction and expansion of the cell volume and the destabilization of the inserted materials derived from the larger size of sodium ions. KEYWORDS: sodium intercalation, sodium ion batteries, Na2Ti3O7, DFT, lithium ion batteries, Li2Ti3O7, lithium intercalation

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INTRODUCTION The development of room temperature sodium based batteries is currently a challenge in fundamental materials research. Although it holds promise for accelerated development thanks to the knowledge gained in the “chemically similar” Li-ion ubiquitous technology, the Na-ion technology is still in its infancy. Proof of the concept was given long ago1,2 but it is only recently that the topic has recaptured the attention of the scientific community concomitant to large scale development of the Li-ion technology and concerns about lithium cost and availability.3−5 This scenario has resuscitated the quest for suitable electrode materials and has also prompted more systematic studies on electrolytes.6,7 Because Na-ion batteries do not involve the use of sodium metal anodes, there would be no a priori reason to think that they cannot attain the same performances as Li-ion batteries, if suitable positive and negative electrode materials are developed. © 2013 American Chemical Society

Along this line, we recently reported on Na2Ti3O7, a wellknown oxide previously studied for a wide range of applications, which turned out to reversibly uptake 2 Na ions per formula unit (200 mAh/g) at an average potential of 0.3 V vs Na+/Na0.8 To our knowledge, this is the first ever reported oxide to reversibly react with sodium at such a low potential, which could tentatively be coupled to any developed high potential positive electrode material to build high energy density Na-ion cells. These preliminary results were inspiring and prompted optimism in terms of technology. However, fundamental understanding of the redox mechanism was lacking and hence further developments in the quest for low potential materials was less straightforward. Even if some recent Received: October 1, 2013 Revised: December 3, 2013 Published: December 4, 2013 4946

dx.doi.org/10.1021/cm4032336 | Chem. Mater. 2013, 25, 4946−4956

Chemistry of Materials

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structures of the reduced A4Ti3O7 phases, which are found to be in good agreement with experimental results.

reports have appeared on other titanates operating at lower potentials,9,10 the A2Ti3O7 case (A = Li, Na) is especially interesting due to the striking differences observed in potentials against lithium and sodium counterelectrodes. The structure of Na2Ti3O7 is built upon TiO6 octahedra linked by edges, so as to form zigzag 3 × 2 × ∞ ribbons.11 These ribbons are connected via vertices and form a layered framework (see Figure 1a).

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METHODOLOGY

Experimental Section. Pure Na2Ti3O7 was prepared from anatase TiO2 (>99.8%, Aldrich) and anhydrous Na2CO3 (>99.995%, Aldrich) mixtures with 10% excess of the latter with respect to stoichiometric amounts. These mixtures were milled and treated at 800 °C for 40h with intermediate regrinding. Li2Ti3O7 was prepared from Na2Ti3O7 through ion exchange, as reported in the literature.12 Typically, LiNO3 (20 molar excess) was ball milled with Na2Ti3O7 for 5 min, and the mixture was heated to 260 °C and kept at that temperature for 2 days. Afterward, it was cooled down to room temperature, washed with ethanol, and dried at 80 °C under air. Electrochemical testing of A2Ti3O7 was carried out in two-electrode Swagelok cells using lithium or sodium (99.9% Aldrich) as a counter electrode in galvanostatic mode. The working electrode consisted of either a powder mixture (70% Na2Ti3O7 or Li2Ti3O7) and 30% SP Carbon (Timcal). Sodium cells were assembled using a 1 M solution of NaClO4 in propylene carbonate (PC) (>99.7% Adrich) as an electrolyte with sodium metal as a counter electrode. Similarly, lithium cells were fabricated using a 1 M electrolyte solution of LiPF6 in EC:DMC and lithium foil as a counter electrode. Stepwise potentiodynamic experiments were carried out with ±5 mV steps and a cut off intensity equivalent to the C/150 galvanostatic rate. Room temperature X-ray powder diffraction patterns were collected using a Bruker D8 laboratory diffractometer with Cu Kα radiation. Additional high-resolution synchrotron powder diffraction patterns were collected on Li2Ti3O7 sealed under Ar in glass capillaries with a 0.5 mm diameter at the 11-BM beamline (λ = 0.4139 Å) at the Advanced Photon Source (Argonne National Lab, mail-in program). Rietveld refinements14 were done using the FullProf program.15 Bond valence sum analysis (BVS) was performed on the obtained structural models using the Zachariasen formula giving the valence of an atom i surrounded by j neighbors at distances dij:

Figure 1. (a) Structure of Na2Ti3O7 perpendicular to the [010] direction (left) and to the [100] direction (right). TiO6 octahedra are colored in blue, O is orange, and Na is shown as yellow balls. (b) Rietveld refinement of Li2Ti3O7 (prepared from Na2Ti3O7) against Synchrotron X-ray diffraction pattern (11BM). Red dots are experimental intensities, the black line is the calculated pattern, and the blue line is the difference between observed and calculated intensities. The vertical green tick marks stand for the Bragg reflections. The structure of Li2Ti3O7 is shown in the inset perpendicular to the [010] direction (left) and to the [100] direction (right). Li is shown as yellow balls.

(d0 − d ij) 0.37

Vi = ∑j s ij = ∑j e

with the parameters d0, characterizing a cation−anion pair, taken from the reference 16. In operando X-ray diffraction (XRD) data were taken using a homemade Swagelok type cell using a Be window17 to avoid exposure to air. Experiments were operated in galvanostatic mode at C/25, with powdered electrodes. The electrolytes used were 1 M LiPF6 in EC:DMC (1:1 in volume) and NaClO4 in PC for cells assembled using lithium and sodium counter electrodes, respectively. Computational Section. Na and Li insertion into A2Ti3O7 (A = Li, Na) were investigated by first principles methods. The total energy calculations and structure relaxations for pristine A2Ti3O7 and intercalated phases A4Ti3O7 were performed with the Vienna Abinitio simulation package (VASP).18,19 Calculations were done within the GGA+U framework with the projector augmented wave (PAW) pseudopotential20 and utilizing the PBE form of exchange-correlation functional.21 The Ti(3p, 3d, 4s) and O(2s, 2p) were treated as valence states. DFT+U calculations were performed following the simplified rotationally invariant form proposed by Dudarev.22 Within this approach, the onsite Coulomb term U and the exchange term J can be grouped together into a single effective parameter, Ueffe, simply referred as U in this paper. A value of U = 3 eV was used for the Ti(3d) states. The energy cut off for the plane wave basis set was kept fixed at a constant value of 600 eV throughout the calculations. The reciprocal space sampling was done with k-point Monckhorst-Pack grids of 4 × 8 × 4 (64 irreducible k-points). Crystallographic models for Na2Ti3O7, Li2Ti3O7, and the intercalated A4Ti3O7 phases were constructed starting from the experimental results of the present work. As a first step, the structures were fully relaxed while keeping the symmetry of the host compound, cell parameters, volume, and atomic positions. For the most stable inserted A4Ti3O7 phases, structure relaxation was further preformed without imposing any symmetry constrain. The final energies of the optimized geometries were

Within this framework, sodium ions are distributed between two distinct crystallographic sites, Na1 and Na2, sitting between the layers; they correspond to the 2e Wyckoff site of monoclinic space group P21/m and are coordinated by 9 and 7 oxygen atoms, respectively. By ion exchange from Na2Ti3O7, Chiba et al.12 could prepare the lithium analogue Li2Ti3O7, which therefore does not exhibit the ramsdellite structure adopted when Li2Ti3O7 is prepared by direct synthesis.13 This new polymorph presents the same structural framework as Na2Ti3O7, with the exception that Li goes in tetrahedral sites between the layers, which would leave empty tetrahedral positions to be occupied by additional lithium atoms. In agreement with such considerations, they confirmed that Li2Ti3O7 could uptake ca. 1.4 additional lithium ions per formula unit at ca. 1.6 V vs Li+/Li0, whereas pristine Na2Ti3O7 was able to insert a much lower amount of lithium atoms (ca. 0.5 per formula unit) at the same potential. Nonetheless, significant capacity fading was observed and site occupancies were not identified at the time. In this paper, we rationalize the differences in potential and capacity observed upon alkali ion intercalation in Na2Ti3O7 and Li2Ti3O7 through density functional theory (DFT) calculations that enable us to propose structural models for the crystal 4947



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recalculated so as to correct the changes in the basis set of the wave functions during relaxation. The atomic relaxation was carried out with the conjugate-gradient algorithm until atomic forces on the individual atoms are below 0.01 eV/Å. All calculations were spin polarized. For comparative purposes, we have computed the average voltages for the insertion of the two alkali ions in two host structures (Na2Ti3O7, Li2Ti3O7). In addition, we have computed the average insertion voltage of 1 alkali ion in ramsdellite-Ti2O4. This ramsdellite polymorph of TiO2 can be prepared by extracting lithium ions at room temperature from the spinel-LiTi2O4 by both chemical and electrochemical methods.23,24 The following insertion reactions were therefore considered:

Na 2Ti3O7 + 2 Li → Li 2‐Na 2Ti3O7

(1)

Na 2Ti3O7 + 2 Na → Na4Ti3O7

(2)

Li 2Ti3O7 + 2 Li → Li4Ti3O7

(3)

Li 2Ti3O7 + 2 Na → Na 2‐Li 2Ti3O7

(4)

Ti 2O4 + Li → LiTi 2O4

(5)

Ti 2O4 + Na → NaTi 2O4

(6)

Table 1. Structural Parameters of Li2Ti3O7 Deduced from the Rietveld Refinement of the Synchrotron Powder Diffraction Patterna P21/m

space group

atom Ti1 Ti2 Ti3 O1 O2 O3 O4 O5 O6 O7 Li1 Li2

Intercalation voltages were computed following the methodology described by Aydinol et al.25

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a (Å) b (Å) c (Å) β (deg) V (Å3) Wyckoff x 2e 2e 2e 2e 2e 2e 2e 2e 2e 2e 2e 2e

0.163(7) 0.266(3) 0.048(4) 0.255(7) 0.180(8) 0.493(4) 0.355(0) 0.010(2) 0.799(3) 0.905(9) 0.600(5) 0.416(8)

y

z

7.5442(7) 3.7520(9) 9.315(1) 97.6138(2) 261.34(7) Biso (Å2)

1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4

0.968(2) 0.659(3) 0.279(9) 0.165(4) 0.449(9) 0.628(1) 0.875(6) 0.756(1) 0.333(2) 0.048(1) 0.829(5) 0.392(2)

0.2(8) 0.4(5) 0.3(6) 0.05(2) 0.05(2) 0.05(2) 0.05(2) 0.05(2) 0.05(2) 0.05(2) 1.8(2) 1.6(2)

BVS 4.137(9) 4.040(9) 4.060(9) 1.860(7) 2.121(9) 1.975(9) 1.927(9) 2.122(3) 2.009(4) 2.058(3) 0.842(7) 0.992(7)

a

Results of a bond valence sum analysis (BVS) are indicated for each atom.

EXPERIMENTAL RESULTS Structure. The structure of our pristine Na2Ti3O7 sample was refined against laboratory X-ray diffraction data using the P21/m space group and lattice parameters a = 8.5642(3) Å, b = 3.8012(1) Å, c = 9.1265(3) Å, and β = 101.597(2)° (V = 291.05(1) Å3) as reported earlier,8 and the resulting structure is shown in Figure 1a (see Table S1 in the Supporting Information for crystallographic data and atomic positions). Li 2Ti 3O 7 made by ion exchange from the latter was characterized by Synchrotron X-ray diffraction (11BM) at room temperature. A Rietveld refinement (Figure 1b) using space group P21/m and unit cell parameters a = 7.5442(7) Å, b = 3.7520(9) Å, c = 9.3148(2) Å, and β = 97.615(1)° (V = 261.34(7) Å3) (Table 1) leads to the structure shown in Figure 1b, in agreement with Chiba’s model. Basically, only the positions of the alkali in the interlayer space differ between Na2Ti3O7 and Li2Ti3O7, as Li is inserted in tetrahedral positions instead of the 7- and 9-coordinated sites for Na. Electrochemical Intercalation. Given the large difference in potential observed for lithium intercalation in Li2Ti3O7 (1.6 V vs Li+/Li0)12 and sodium intercalation in Na2Ti3O7 (0.3 V vs Na+/Na0),8 intercalations of lithium into Na2Ti3O7 and sodium into Li2Ti3O7 were also attempted and all processes were followed through in situ XRD, as will be shown later. The potential vs composition profiles for sodium and lithium intercalation in Na2Ti3O7 are shown in Figure 2. In the first case, an irreversible pseudoplateau is observed at 0.7 V vs Na+/ Na0, which is due to the parasitic reaction of electrolyte with SP carbon present in the electrode. Further reduction takes place with the observation of a reversible plateau around 0.3 V vs Na+/Na0 with concomitant intercalation of ca. two sodium ions in the structure (i.e., reduction of 2/3 of Ti(IV) to Ti(III) through a two phase mechanism, as revealed by in situ XRD and electrochemical experiments8). Concerning lithium intercalation, a pseudoplateau is observed at 1.6 V vs Li+/Li0 followed by a gradual decrease in potential, corresponding to an exchange of 1.1 electrons per mol of Na2Ti3O7. Upon subsequent oxidation, the pseudoplateau at 1.7 V vs Li+/Li0 is only partially reversible (0.6 electrons

exchanged per mol of Na2Ti3O7) in full agreement with results achieved by Chiba et al.12 A decrease in the cut off potential (Figure 2c) does result in the observation of a sloppy potential decrease, most likely entailing some irreversible transformation of the phase (note that the profile upon further oxidation is drastically changed and the capacity severely diminished) coupled also to electrolyte decomposition close to 0 V, in agreement with the gradual shift of the curves upon cycling. Figure 3 depicts the potential versus capacity profile for sodium and lithium intercalation into Li2Ti3O7. In the first case, the potential monotonously decreases down to 0.9 V vs Na+/ Na0 and a plateau at 0.7 V is observed upon further reduction, followed by final voltage decay to 0 V, similar to what was observed for full reduction of Na2Ti3O7 against lithium counterelectrodes, which is in agreement with the same (Na,Li)2+xTi3O7 being formed at the end of reduction. Overall insertion/deinsertion of 2 mol of sodium per mol of Li2Ti3O7 is achieved during the first cycle, which entails an irreversible transformation at a very low potential because the profile for the second reduction is completely different from that of the first one. In the case of lithium intercalation into Li2Ti3O7 (Figure 3b), a plateau at 1.6 V vs Li+/Li0 is observed upon reduction followed by voltage decay up to 1.0 V overall, accounting for an exchange of 2.2 mol of electrons per mol of Li2Ti3O7. On the subsequent oxidation, the potential-composition profile becomes sloppier with 1.6 mol of electrons per mol of Li2Ti3O7 being reversibly exchanged. Such results are again fully consistent with the previous studies by Chiba et al.12 The derivative curve (not shown) seems to point at a different reaction pathway upon reduction and oxidation. Indeed, a single peak is observed at 1.6 V vs Li+/Li0 upon reduction and at least two partially overlapping peaks at ca. 1.72 and 1.85 V are observed upon oxidation. Results of stepwise potentiodynamic experiments using the electrochemical potential spectroscopy (EPS) protocol of Thomson26 (Figure 3c) are in full agreement with such observations, because the current 4948



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Figure 2. Potential vs composition profiles for (a) Na2Ti3O7/Na cell cycled in 1 M NaClO4 in PC between 0 and 2.5 V (the blue curve corresponds to a blank experiment in which only the carbon additive is present in the working electrode) and Na2Ti3O7/Li cells cycled in 1 M LiPF6 in EC:DMC between (b) 1−2.5 V and (c) 0−2.5 V at C/25.

Figure 3. Potential vs composition profiles for (a) Li2Ti3O7/Na cell cycled in 1 M NaClO4 in PC electrolyte between 0 and 2.5 V and (b) Li2Ti3O7/ Li cell cycled in 1 M LiPF6 in EC:DMC electrolyte between 1.0 and 2.5 V. (c) Stepwise potentiodynamic experiment of Li2Ti3O7/Li cell with ±5 mV steps and a cut off intensity equivalent to C/150 (the continuous red line corresponds to potential and blue scattered points to current).

On the first reduction, the peaks of the pristine Li2Ti3O7 phase at 2θ = 12.0°, 16.4°, 26.8°, 29.2°, 33.1°, and 38.9° diminish in intensity concomitantly to the appearance and growth of a new set of reflections at 2θ = 13.5°, 17.8°, 25.7°, 29.6°, 30.9°, 37.0°, and 44.2°, which clearly shows that lithium insertion into Li2Ti3O7 follows a two-phase redox mechanism (patterns in black). At the end of reduction (pattern in green), the composition of the phase could be estimated as Li3.6Ti3O7, in good agreement with observations by Chiba et al.10 Upon subsequent oxidation, the peaks of the reduced phase diminish and a set of peaks at 2θ = 12.0°, 16.5°, 17.1°, 26.5°, 29.0°, 29.3°, 29.8°, and 39.0° grow (patterns in red). Even if the electrochemical experiments seemed to indicate the presence of at least one intermediate phase upon oxidation, which would have a narrow existence range (between ca. 1.72 and 1.85 V), the resolution of the patterns and the conditions of the experiment did not allow us to detect them. At the end of first oxidation, the XRD pattern of reoxidized electrode (pattern in brown) shows some pronounced differences when compared to the pristine phase, in agreement with results from electrochemical experiments indicating that the mechanism of redox transformation occurring upon the first reduction was not fully reversible. In particular, the peak at 2θ = 12.0° corresponding to (1 0 0) reflection of the pristine phase does exhibit a very low intensity compared to what expected. This is only in partial agreement with the findings of Chiba et al. since they do also report the potential-composition curve becoming sloppier but do mention that almost all reflections were observed and no extra peaks were detected in agreement with the structural framework not being damaged. In situ XRD was also carried out to follow lithium insertion in Na2Ti3O7 and sodium insertion in Li2Ti3O7. The XRD

response during the first reduction does not follow the Cottrelllike behavior expected from a single phase mechanism. Nonetheless, the behavior upon oxidation seems to proceed through a different process. The composition of the fully reduced phase can be estimated to be Li3.6Ti3O7 and the irreversible capacity can be attributed to the parasitic reaction of electrolyte with carbon additive. To grasp further understanding on this phenomenon, we have carried out in situ XRD on Li2Ti3O7 during galvanostatic cycling against lithium metal as a counter electrode (Figure 4).

Figure 4. Selected patterns from in situ XRD of a Li2Ti3O7/30 wt % C electrode cycled against lithium metal in 1 M LiPF6 in EC:DMC electrolyte between 2.5 and 1.4 V vs Li+/Li0 at C/25. The pink arrows represent the additional peaks in the XRD pattern of reoxidized electrode in comparison with pristine Li2Ti3O7. 4949



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patterns of the reduced “LixNayTi3O7” phases are similar to the one of Li3.6Ti3O7, as shown in Figure 5. Interpretation of such

Na2Ti3O7, taken from our previous paper.8 Even if the patterns of the four reduced phases mentioned above show a different signal-to-noise ratio derived from different counting times, the similarities between all profiles are evident, except the position of the peaks being significantly shifted for the case of Na4Ti3O7. While in our previous study we reported on the similarity of its XRD pattern to that of Na16Ti10O28, in light of the present results, this seems, retrospectively, to be purely coincidental, as will be shown next. We are therefore tempted to conclude that starting with the same structural framework consisting of zigzag [Ti(IV)3O7]2− layers, intercalation of alkali cations involving the Ti(IV)/Ti(III) redox couple involves the formation of reduced phases with related structures even if occurring at notably different potentials. Aside from the differences in the initial structures, i.e., sodium and lithium ions, respectively, occupying 7/9-coordinated and tetrahedral sites in between [Ti3O7]2− layers, knowledge of the crystal structure of the reduced phases is compulsory in order to rationalize the potential differences observed. Several attempts were made to characterize Li3.6Ti3O7 and Na4Ti3O7 by either recovering electrochemically reduced phases or attempting chemical reduction of Li2Ti3O7 and Na2Ti3O7 at room temperature using n-buthyl lithium in n-hexane and naphtyl sodium in tetrahydrofuran as reducing agents. All such experiments were unsuccessful and yielded a mixture of A4Ti3O7 and A2Ti3O7, only A2Ti3O7, or amorphous products.

Figure 5. XRD patterns (background subtracted) of the phases obtained at the end of electrochemical reduction for (i) Na2Ti3O7 against a sodium counter electrode to yield Na4Ti3O7 (ii) Na2Ti3O7 against a lithium counter electrode to yield a phase with nominal composition “Li0.6Na2Ti3O7”, (iii) Li2Ti3O7 against a sodium counter electrode to yield a phase with nominal composition “Na2Li2Ti3O7”, and (iv) Li2Ti3O7 against a lithium counter electrode to yield Li3.6Ti3O7. Peaks tentatively ascribed to unreacted Na2Ti3O7 and Li2Ti3O7 are denoted with * and # symbols, respectively.

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COMPUTATIONAL RESULTS Na2Ti3O7. Considering the insertion of two Na atoms in Na2Ti3O7 from a crystal chemistry point of view, the possibilities to place Na atoms in the Ti3O7 framework are presented in Figure 6. In addition to the two sodium ions (Na1

results is complex because (i) lithium and sodium ions are not expected to occupy the same crystal site due to their size difference and (ii) exchange between the alkali ions present between the layers and those present in the electrolyte prevents reliable estimations of the stoichiometry of the phases in terms of lithium to sodium ratio, which may lead to the observation of different redox phenomena depending on the degree of exchange. Nonetheless, some general trends can be observed and lithium insertion in both Li2Ti3O7 and Na2Ti3O7 takes place at 1.6 V vs Li+/Li0, as could be expected for Ti(IV)/ Ti(III) redox couple operation. The larger lithium insertion capacity for Li2Ti3O7 than for Na2Ti3O7 (1.6 mol vs 0.6 mol) may be due to the large sodium ions present in 7/9coordinated sites in the interlayer space, blocking lithium ion intercalation. Now turning to sodium insertion, Li2Ti3O7 uptakes ca. 1 mol of sodium atoms above 1 V vs Na+/Na0 to form the same type of “LixNayTi3O7” intermediate achieved through lithium intercalation in Na2Ti3O7. Below this potential, sodium intercalation is observed for both Li2Ti3O7 and Na2Ti3O7 at about 0.3 V vs Na+/Na0. Nonetheless, real sodium intercalation at a low potential in a structural framework keeping a significant amount of lithium ions cannot be unambiguously postulated, because ion exchange with the electrolyte ions is expected to be significant. In agreement with this, in situ XRD results indicate that Li2Ti3O7 is present in the electrode at the end of a full reduction−oxidation cycle for Na2Ti3O7 in the lithium containing electrolyte. The degree exchange does not seem to be related to relative sizes of both ions but to be induced by the large ion concentration in the electrolyte. Indeed, Na2Ti3O7 is observed at the end of a full reduction−oxidation cycle for Li2Ti3O7 tested in the sodium containing electrolyte. Figure 5 also gathers the XRD pattern of electrochemically reduced Na4Ti3O7 taken in situ from Na insertion into

Figure 6. Crystal structure of Na2Ti3O7 with TiO6 octahedra colored in blue and sodium atoms shown as balls. Yellow balls labeled 1 and 2 represent Na1 and Na2 atoms in between the layers in Na2Ti3O7. Light blue balls labeled as 3, 4, 5, and 6 are the other possible sites (Na3−Na6) to intercalate Na ions that were considered in the Na4Ti3O7 models for DFT calculations.

and Na2) already present in the pristine structure, one may imagine that some sodium atoms may occupy the Na3 2d (1/2, 0, 1/2), Na4 4f (0.59, 1/2, 0.72), Na5 2b°(1/2,°0,°0), and Na6 2c (0, 0, 1/2) positions. Na3, Na4, and Na5 are located between the layers, whereas Na6 is in the middle, between the pivot oxygen atoms that connect adjacent ribbons to form layers. The multiplicity of all these positions is 2, except for Na4, which is in the 4f Wyckoff site. We therefore have created 11 structural models for Na4Ti3O7, by placing eight sodium ions among these six possible crystallographic positions. They 4950



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are denoted 1235 (sodium atoms placed on the Na1, Na2, Na3, and Na5 positions), 124, 1236, 1256, 134, 1356, 234, 2356, 345, 346, 456. Most of them present unrealistic distances between cations and should be seen only as starting models that should be relaxed through DFT calculations. Na−Na distances are of the order of 1.7 Å, less than twice the Na ionic radii (1.02 Å), which is extremely short to form stable structures. In contrast, Ti−Na distances are close to 3 Å, which should not bring in any cationic repulsion that could compromise the stability of the structure. One can also note that the first three models are just created by adding sodium ions without modifying the positions of the pristine Na1 and Na2, whereas the others imply that Na1 and/or Na2 empty at the benefit of some other positions. The total energies for the 11 structural models of Na4Ti3O7 were calculated, allowing the relaxation of atomic positions, cell parameters, and cell volume, while keeping the symmetry of the initial phase. In all the models, Na insertion produces the reduction of four out of the six Ti(IV) ions to Ti(III), and a volume expansion ranging from 13% (1256 model) to 28% (456 model). The intercalated phases are predicted to be semiconductor compounds with band gaps of the order of 0.5 eV. For the initial Na2Ti3O7, the calculated band gap is of 3.3 eV, close to the experimental value of 3.7 eV.27 Figure 7 compares the calculated total energy for all models taking, as the zero of energy, the total energy of the most stable configuration.

models present too short of Na−Na distances, with some Na ions being only about 2 Å apart from each other (see Table 2). Table 2. Calculated Shortest A−A distances Found in the Optimized Structures of the Host Compounds, Na2Ti3O7 and Li2Ti3O7, and Their Lithium/Sodium Intercalated Phases (124 model) after a First Relaxation Step and after Full Optimization Na−Na (Å) host-Na2Ti3O7 host-Li2Ti3O7 intercalated phases after the first relaxation process (124 model) Na2-Na2Ti3O7 Li2-Na2Ti3O7 Li2-Li2Ti3O7 Na2-Li2Ti3O7 intercalated phases fully optimized Na2-Na2Ti3O7 Li2-Na2Ti3O7 Li2-Li2Ti3O7 Na2-Li2Ti3O7

Li−Li (Å)

Na−Li (Å)

calcd voltage (V)

3.5201 2.73

2.0582 2.9128 2.0513

2.9854 3.0896 3.0044

2.1312 2.1126 2.8471

2.5308

2.8841 2.8199 2.7606

2.7590

2.8409

2.8233

−0.8 0.09 0.38 −0.93

0.37 0.90 1.46 0.77

The crystal structures of the most likely models of Na4Ti3O7 (124 and 1236) are shown in the upper panel of Figure 8. The Ti−O framework is very similar, except that for the 1236relaxed model, one Ti−O bond that bridges two adjacent ribbons becomes very long, so that if we exclude it in a polyhedral view, the ribbons are not connected to form layers. Both models were further investigated, and a new set of DFT calculations was performed allowing a full structure relaxation without imposing any symmetry constrain. After the full relaxation, the total energy of the two investigated models drastically drops down, yielding a calculated sodium insertion average voltage of 0.37 V for both the 124 and 1236 models. This value agrees well with the experimentally observed voltage of 0.3 V. The two final optimized structures have the same total energy and lattice parameters. The search for pseudosymmetry in the final optimized 124 and 1236 models was done using the Bilbao Crystallographic Server (program PSEUDO)28 and we could, for both of them, describe the models back in the P21/m space group. Even if the two starting models radically differ in the Na positions, the resulting structure, after full DFT optimization, indicates that the sodium ions go to the same positions for both 124 and 1236 fully optimized structures. Sodium ions (relabeled as Na1, Na2, Na3, and Na4) are all on 2e Wyckoff site positions being (x, 1/4, z) and (−x, 3/4, −z), each with different (x, z) values. The Ti−O framework is also the same for 124 and 1236 fully relaxed structures, with disappearance of the strong distortion of some TiO6 octahedra observed for the latter after the initial optimization. Thus, as shown in Figure 8, the full optimization of both models converges to a unique structure with an unaltered/preserved Ti−O framework where the Na ions have migrated from some of their initial positions (124 or 1236) to more stable sites, enabling larger Na−Na distances (see Table 2). The corresponding internal atomic coordinates in the P21/m space group are reported in Table 4. As summarized in Table 2, the shortest Na−Na distances have increased from 1.77 Å (initial

Figure 7. Calculated total energy for the 11 possible models for A4Ti3O7 (A = Li, Na). Blue filled and green empty symbols indicate A = Li and Na, respectively.

The most stable configuration is found to be the 124, where the initial Na positions (sites Na1 and Na2) are occupied together with the Na4 site of multiplicity 4. Other models that keep the initial positions occupied (models 1236, 1256) are also quite stable. On the contrary, the energy difference increases to about 3 eV/fu for the less stable models, in which the Na1 and Na2 sites are empty (346 and 2356 models). This notorious difference indicates that the energetic stability of the intercalated phase is largely controlled by the crystallographic position occupied by Na ions. As a result, the calculated electrochemical voltage of reaction 2 spans in a wide range from −2.4 V (2356 model) to −0.8 V (124 model). A negative voltage signifies that none of the intercalated phases are stable enough as to thermodynamically favor the sodiation reaction of Na2Ti3O7. We should note that these optimized Na4Ti3O7 4951



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Figure 8. Crystal structure of the 124 and 136 models for Na4Ti3O7 after first relaxation process compared to the fully optimized structure (view along the [010] axis). TiO6 octahedra are colored in blue and sodium atoms are shown as yellow balls.

Table 3. Calculated Lattice Parameters and Unit Cell Volumes for the Host Compounds Na2Ti3O7 and Li2Ti3O7 and Their Lithium/Sodium Intercalated Phasesa a (Å)

compound host-Na2Ti3O7 Na4Ti3O7 Li2-Na2Ti3O7 host-Li2Ti3O7 Li4Ti3O7 Na2-Li2Ti3O7 a

8.646 7.472 7.255 7.651 6.817 7.691

(8.5642(8)) (7.309(3)) (7.5442(7)) (6.749(9))

b (Å) 3.867 4.442 4.284 3.813 4.198 4.222

(3.8012(1)) (4.381(2)) (3.7520(9)) (4.115(6))

α, β, γ (deg)

c (Å) 9.280 9.802 9.688 9.488 9.447 9.661

(9.1265(3)) (9.664(5)) (9.3148(2)) (9.249(6))

90, 90, 90, 90, 90, 90,

101.7, 90 (101.597(2)) 97.87, 90 (97.32(2)) 98.23, 90 97.33, 90 (97.6138(2)) 98.65, 90 (97.85(4)) 100.39, 90

V (Å3) 303.84 322.27 297.97 274.60 267.29 308.60

(291.05(1)) (306.94(22)) (261.34(7)) (253.79(6))

Experimental data (space group P21/m) are given in parentheses.

experiments and the value reported by Chiba et al.12 The calculated lattice parameters (Table 3) and atomic distances for Li2Ti3O7 are also in good agreement with those of Chiba.12 Lithium insertion causes a volume contraction of 2.6% (see Table 3), an interesting fact to be later compared to experimental results. Mixed A4Ti3O7 Compounds. For completeness, we have investigated the insertion of two additional lithium ions in Na2Ti3O7 (Li2-Na2Ti3O7) and two additional sodium ions in Li2Ti3O7 (Na2-Li2Ti3O7), corresponding to reactions 1 and 4. For the crystal structure of the inserted phases (Li2-Na2Ti3O7 and Na2-Li2Ti3O7), we have considered (1) the 124 model and (2) the final optimized structures found for Na4Ti3O7 and Li4Ti3O7, where all the alkali ions occupy octahedral sites. The 124 model yields low insertion voltages and too short A−A distances, whereas more reasonable values are predicted for the second structure (see Table 2). Thus, lithium insertion in Na2Ti3O7 causes a volume contraction of 2% whereas sodium insertion in Li2Ti3O7 is accompanied by a notorious volume expansion of 12%. Such a large predicted value suggests that a phase transformation could occur at some point during the insertion reaction. The calculated average voltages are 0.77 V for reaction 4 and 0.9 V for reaction 1. Unfortunately, confrontation to experimental values is prevented due to ion exchange, as discussed above.

model) to 2 Å (first relaxation) and to 2.9 Å (optimized structure). Calculated lattice parameters for Na2Ti3O7 and Na4Ti3O7 are given in Table 3. Upon intercalation, a moderate volume expansion of 6% is predicted, in agreement with the presence of the larger reduced transition metal cations (Ti3+ vs Ti4+), together with the additional inserted sodium ions. Li2Ti3O7. To investigate the insertion of additional lithium ions in Li2Ti3O7, we have also computed the 11 possible models above-described for the analogous sodium case. Figure 7 shows the calculated total energies. Interestingly, qualitatively speaking, the relative stability of the A4Ti3O7 intercalated phases is similar for both Li and Na ions, which points to the occupancy of certain sites (2356, 345, 346...) destabilizing both host structures. However, the energy differences are much lower for the smaller lithium ions, which seem to be easier to accommodate between the layers. The 124-Li model is the most stable one. However, as encountered for the sodium case, the relaxation of any of the 11 models results in too low of intercalation voltages, ranging from −0.47 V (346 model) to +0.38 V (124 model). Allowing a full structural optimization without symmetry constrains again produces a much more stable Li4Ti3O7 structure, where lithium ions have relocated with respect to the initial 124 model (see Table 5 for their position in space group P21/m). A detailed crystallographic analysis reveals that the final Li4Ti3O7 phase is isostructural with Na4Ti3O7, with all lithium ions occupying octahedral sites. As discussed for Na2Ti3O7, the displacements of lithium ions and, in general, the structural rearrangement permits an increase of the Li−Li distances, therefore diminishing electrostatic repulsions (see Table 2). While after the first relaxation, the shortest Li−Li distance is 2.11 Å, it increases to 2.83 Å in the final Li4Ti3O7 structure. Considering the calculated total energy of the final Li4Ti3O7 phase, the calculated average lithium insertion voltage for reaction 3 is 1.46 V, in quite good agreement with our

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DISCUSSION Crystal Structure of the Reduced Phases. Because the reactivity of the reduced phases did not allow their isolation as pure compounds, the only way left to get an insight on their structure was to directly work on the in situ patterns and try to extract as much information as possible even if the patterns being recorded behind a beryllium window, and the small exploitable 2θ angular range preclude the possibility of any standard Rietveld refinement. Thus, we decided to confront our experimental XRD pattern with the final structural models 4952



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resulting from DFT calculations. No refinement of the atomic coordinates was carried out but rather a comparison of the calculated intensities and the experimental ones. As GGA based calculations are known to overestimate the unit cell parameters, the agreement between the simulated and observed patterns was very poor at a first sight. However, knowing the structural model and the expected intensities of reflections, the lattice parameters were varied step by step, which allowed us to gradually approach a nice agreement with the experimental pattern. A comparison of the experimental pattern and the simulated one with the same peak broadening is displayed Figure 9a. The structural model and lattice parameters used to describe Na4Ti3O7 are given in Table 4. As the pattern is not of enough quality to allow a refinement of the atomic positions, these were kept to the optimized DFT values and only the lattice parameters were refined. When the structures of Na4Ti3O7 and Na2Ti3O7 are compared, the Ti−O framework

Table 4. Crystallographic Data and Atomic Positions for Na4Ti3O7 Resulting from Refinement of the Unit Cell Parameters with Atomic Coordinates Obtained from DFT Calculations Using XRD Data Collected in situa space group

P21/m

atom

a (Å) b (Å) c (Å) α (°) β (deg) γ (deg) V (Å3) Wyckoff

x

y

7.309(3) 4.381(2) 9.664(5) 90 97.32(2) 90 306.94(22) z

BVS

Ti1 Ti2 Ti3 O1 O2 O3 O4 O5 O6 O7 Na1 Na2 Na3 Na4

2e 2e 2e 2e 2e 2e 2e 2e 2e 2e 2e 2e 2e 2e

0.0101 0.2758 0.1494 0.2429 0.1431 0.5114 0.3675 0.0208 0.7531 0.8918 0.4413 0.5595 0.8377 0.7078

1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4

0.7671 0.1694 0.4651 0.6529 0.9486 0.1287 0.3963 0.2629 0.8155 0.5417 0.8918 0.6129 0.0413 0.3194

2.7 2.6 3.3 2.2 2.2 2.3 2.2 2.0 2.1 1.9 1.4 1.3 1.5 1.5

a

Results of a bond valence sum analysis (BVS, see text) are also displayed.

is maintained, as compared to Na2Ti3O7, but the sodium distribution within the unit cell differs. In particular, we note that to accommodate the two additional sodium ions, the pristine two sodium ions in Na2Ti3O7 are displaced from their initial position (by about 0.7 and 1.5 Å for Na2 and Na1, respectively) and their coordination number is reduced from 9 (Na1) and 7 (Na2) to 6. Insertion of two additional sodium ions then induces a collective rearrangement of the Na sublattice. In Na4Ti3O7, sodium ions lie in the middle of edge-sharing distorted octahedra with Na−O distances ranging from 2.16 to 2.8 Å, (see Figure S1 in the Supporting Information). Results of a bond valence sum analysis confirm that the Ti are close to the +3 oxidation state (Table 4) whereas values between +1.3 and +1.5 are obtained for Na atoms. These are unexpectedly high, but we ascribe this to the fact that these values are deduced from a structure which has not been Rietveld refined. Last, we can note that the unit cell volume experimentally increases by 5%, in agreement with DFT predictions. Figure 9b shows the good agreement between the XRD experimental pattern of Li3.6Ti3O7 measured in situ after full reduction of the cell, and the simulation using the model obtained from DFT with lattice parameters adjusted against observed peak positions. The resulting cell parameters and atomic coordinates are given in Table 5. In contrast to sodium intercalation into Na2Ti3O7, lithium insertion into Li2Ti3O7 causes a decrease in the volume of the unit cell (2.9%), which is again in excellent agreement with computational predictions. Li(1) and Li(2) in Li3.6Ti3O7 are shifted by 2.5 and 2.6 Å, respectively, with respect to their positions in pristine Li2Ti3O7 and have shifted from tetrahedral to octahedral sites in the reduced phase with a collective rearrangement of lithium

Figure 9. Comparison of in situ XRD patterns of (a) Na4Ti3O7 and (b) Li4Ti3O7 and the simulation based on the fully optimized model for A4Ti3O7 (see text for more details). Red dots are experimental points and the black line indicates the calculated pattern with lattice parameters adjusted against experimental peak positions. Vertical tick bars indicate Bragg reflections for space group P21/m. 4953



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Table 5. Crystallographic Data and Atomic Positions of “Li4Ti3O7” Resulting from Refinement of the Unit Cell Parameters with Atomic Coordinates Obtained from DFT Calculations Using XRD Data Collected in situa space group

P21/m

atom

a (Å) b (Å) c (Å) β (deg) V (Å3) Wyckoff

x

y

6.749(9) 4.115(6) 9.249(6) 97.85(4) 253.79(6) z

BVS

Ti1 Ti2 Ti3 O1 O2 O3 O4 O5 O6 O7 Li1 Li2 Li3 Li4

2e 2e 2e 2e 2e 2e 2e 2e 2e 2e 2e 2e 2e 2e

0.0306 0.2895 0.1558 0.2728 0.1870 0.5446 0.4027 0.0177 0.7455 0.8876 0.7875 0.5457 0.4312 0.6660

1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4

0.7639 0.1560 0.4601 0.6714 0.9596 0.1286 0.3841 0.2408 0.8334 0.5438 0.0551 0.6032 0.8682 0.3315

3.0 3.7 3.1 2.1 2.1 2.1 2.0 2.0 1.8 2.0 1.1 0.9 1.1 1.1

Figure 10. Representation of the A4Ti3O7 structure (A = Li, Na). AO6 octahedra are colored in yellow, TiO6 octahedra are blue, and O is orange. The structure can be seen as rocksalt related due to the connection of octahedra through edges only.

also becomes essential to have a quite flexible framework, capable of undergoing structural changes so as to create new sites or adapt those existing to the intercalated ions. Intercalation Potential. It is usually assumed that the intercalation potential of a given material for sodium ions against sodium metal should lie 0.3 V below that of lithium ions against lithium metal. Such difference emerges from comparing the metal standard reduction potentials (Li+/Li = −3.04 V vs NHE, Na+/Na = −2.71 V vs NHE) tabulated in a 1 M aqueous solution, conditions that are not practical in alkali-ion batteries. This issue has been nicely discussed by Ceder and co-workers, who demonstrated that there is a quite strong dependence of the difference between Li and Na intercalation voltages (VLi − VNa) with the crystal structure. For alkali (Li, Na) ions intercalated in the same structure, they found that Li insertion voltages are higher than Na insertion voltages in 0.57 V for layered AxMO2 and in 0.39 V for olivine AxMPO4 (0 < x 0) indicates that sodiation yields a less stable compound than lithiation. A logical reasoning recognizes the larger Na+ (rVINa+ = 1.02 Å, rVILi+ = 0.76 Å) as the first destabilizing agent in most frameworks. Furthermore, the type of site occupied by the inserted alkali is also a relevant factor. Occupation of tetrahedral sites, which are very favorable for lithium but not for sodium ions, will induce the larger values of VLi − VNa. A large potential difference of 0.78 V is predicted for the ramsdellite−Ti2O4, where alkali ions occupy tetrahedral sites (see Table 6), because occupation of the small tetrahedral sites makes NaTi2O4 much more destabilized than LiTi2O4 with respect to the Ti2O4 host. On the other extreme, occupation of sites with high coordination numbers, which could accommodate sodium but not lithium, would penalize the energy of lithiated compounds with respect to that of sodiated compounds, hence decreasing the potential difference VLi − VNa. To illustrate this, we have calculated the average potential for the virtual reaction of a rhenium based perovskite: ReO3 + A → AReO3 (cubic perovskite)(A = alkali − ion) (9)

Predicted GGA values are 1.9 V for Na and 1.6 V for Li. Here VLi − VNa turned out to be negative (−0.3 V) because alkali ions would enter in a large site (coordination number = 12), extremely unfavorable for Li ions (indeed, LiReO3 does not exist as a cubic perovskite). 4955



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(23) Akimoto, J.; Gotoh, Y.; Oosawa, Y.; Nonose, N.; Kumagai, T.; Aoki, K.; Takei, H. J. Solid State Chem. 1994, 113, 27−36. (24) Kuhn, A.; Amandi, R.; García-Alvarado, F. J. Power Sources 2001, 92, 221−227. (25) Aydinol, M. K.; Kohan, A. F.; Ceder, G.; Cho, K.; Joannopoulos, J. Phys. Rev. B 1997, 56, 1354−1365. (26) Thompson, A. H. J. Electrochem. Soc. 1979, 126, 608−616. (27) Pan, H.; Lu, X.; Yu, X.; Hu, Y.-S.; Li, H.; Yang, X.-Q.; Chen, L. Adv. Energy Mater 2013, 3, 1186−1194. (28) Capillas, C.; Tasci, E. S.; de la Flor, G.; Orobengoa, D.; PerezMato, J. M.; Aroyo, M. I. Z. Z. Kristallogr. − Cryst. Mater. 2011, 226, 186−196. (29) Arroyo-de Dompablo, M. E.; Morales-García, A.; Taravillo, M. J. Chem. Phys. 2011, 135, 054503. (30) Ong, S. P.; Chevrier, V. L.; Hautier, G.; Jain, A.; Moore, C.; Kim, S.; Ma, X.; Ceder, G. Energy Environ. Sci. 2011, 4, 3680−3688.

ASSOCIATED CONTENT

S Supporting Information *

Crystallographic data and atomic positions for Na2Ti3O7 and coordination around sodium ions in Na4Ti3O7. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*M. Elena Arroyo y de Dompablo. E-mail: e.arroyo@quim. ucm.es. ́ E-mail: [email protected]. *M. Rosa Palacin. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to ALISTORE-ERI members for fruitful discussions and acknowledge Ministerio de Ciencia e Innovación for grants MAT2011-24757, MAT2011-22753, and CSD2007-00045.

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