Structure and Dynamics of Fluorophosphate Na-Ion Battery Cathodes

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Structure and Dynamics of Fluorophosphate Na-Ion Battery Cathodes Stephen T. Dacek,† William D. Richards,† Daniil A. Kitchaev,† and Gerbrand Ceder*,†,‡,§ †

Department of Materials Science and Engineering, MIT, Cambridge, Massachusetts 02139, United States Materials Science Division, LBNL, Berkeley, California 94720, United States § Department of Materials Science and Engineering, UC Berkeley, Berkeley, California 94720, United States ‡

ABSTRACT: Fluorophosphate cathodes with the chemical formula NaxV2(PO4)2O2yF3−2y (0 ≤ x ≤ 4, 0 ≤ y ≤ 1) are some of the few known sodium-ion cathode materials with the potential to be competitive with conventional lithium-ion cathodes. However, the experimentally accessible performance of the fluorophosphates remains limited, primarily due to the fact that only half of the theoretical capacity has been reversibly cycled. In this article, we review the extensive body of literature on the fluorophosphate class of sodium-ion cathodes and, in combination with our own ab initio model of the material, investigate the mechanisms underlying the sodium-extraction limitations in the NaxV2(PO4)2F3 (y = 0) fluorophosphate. Specifically, we focus on the potential to reversibly extract sodium beyond the 1 ≤ x ≤ 3 range. We find that this limitation arises from a combination of the high voltage of the V4+/5+ oxidation reaction associated with sodium extraction in the 0 ≤ x ≤ 1 region and a precipitous drop in sodium diffusivity near the x = 1 composition due to the presence of a strong ordering, which prevents the formation of mobile defects in the structure. We conclude that the accessible capacity of NaxV2(PO4)2F3 can potentially be expanded to 0 ≤ x ≤ 3 by introducing defects into the material and reducing the voltage of the transition metal redox couple, both of which can likely be achieved via transition metal substitution and aliovalent anion doping. synthesized structure could be reversibly extracted.3,25,26 While one study reported potential extraction of sodium beyond the x = 1 limit when cycled in a Li electrolyte versus a Li metal anode,26 to the best of our knowledge no experiments have reported a reversible extraction and insertion of pure sodium beyond the x = 1 sodiation level. In order for sodium fluorophosphate cathodes to be viable, the accessible Na capacity must be extended. The sodium extraction limit at x = 1 has been attributed to the high voltage of the V4+/5+ redox couple, predicted to be near 5 V,7,27 which exceeds the stability range of current Na electrolytes.28,29 However, recent results indicate that independent of electrolyte stability issues, the V4+/5+ redox couple is active and accessible in Na3V2(PO4)2O2F and Na3VGa(PO4)2F3.4,7 Thus, the extraction limit is not intrinsic to the active vanadium redox state but is instead likely tied to a more subtle mechanism related to the accessibility of Na sites.4 One hint to the nature of the limiting mechanism is the experimentally reported fall in Na chemical diffusivity around x = 1 and x = 3.20 However, the drop in diffusivity has similarly eluded explanation as both calculated and measured sodium diffusion barriers at these concentrations are small.6,7 Thus, any effort to design a

1. INTRODUCTION Advances in reversible electrochemical energy storage in the decades following the commercialization of the first Li-ion batteries have defined the sustainable energy landscape, enabling the electrification of vehicles, grid-scale utilization of intermittent energy resources, and the spread of portable electronics. Given the wide range of applications, the search for improved performance and reliability in batteries has been an active research topic. A promising new direction in the field which has re-emerged in the past few years is the possible switch from Li-ion to Na-ion chemistries, as sodium may alleviate concerns of Li-resource availability, expand the range of candidate cathode materials, and improve rate capabilities and battery lifetime.1 One of the most promising classes of cathode materials for Na-ion batteries are the fluorophosphates, with a 4 e−/f.u. theoretical capacity of 243 mAh/g,2 high average voltage,3,4 small voltage polarization,5 and low volume change on cycling.6−9 Shortly following the characterization of the material framework Na3M2(PO4)2F3 by Le Meins et al.10−12 and Na3M2(PO4)2O2F by Massa et al.,13 experimental studies demonstrated clear room for improvement in accessible capacity: although near 2 e−/f.u theoretical capacity (up to 126 out of 128 mAh/g) was consistently accessible on partial sodium cycling within the 1 ≤ x ≤ 3 range for NaxM2(PO4)2F3,6,7,14−24 only 2/3 of the sodium in the as© 2016 American Chemical Society

Received: May 17, 2016 Revised: July 14, 2016 Published: July 14, 2016 5450

DOI: 10.1021/acs.chemmater.6b01989 Chem. Mater. 2016, 28, 5450−5460

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Chemistry of Materials

Figure 1. (a) Convex hull of the NaxV2(PO4)2F3 system reported in eV/fu. Na3V2(PO4)2F3 and V2(PO4)2F3 have been chosen as the reference compositions. (b) The computed voltage curve of NaxV2(PO4)2F3 across the entire 0 ≤ x ≤ 4 sodiation range. Note that as discussed in the Methods section, the true voltage of the material is expected to be consistently 0.4 V higher than the computed voltage, as shown by the gray voltage curve.

fluorophosphate-class sodium cathode capable of cycling sodium within the 0 ≤ x ≤ 3 sodiation range will need to address both the problem of the high voltage needed to drive the reaction and the kinetic obstacles to extraction near the x = 1 sodiation level, motivating an in-depth investigation of the mechanisms underlying both the thermodynamic and kinetic features of the material. Previous attempts to improve the performance of the fluorophosphates have focused on substitutions on the anion and transition metal sublattices, as well as synthesis optimization. Modification of the anion sublattice has resulted in the investigation of isostructural materials of the Na3V2(PO4)2X class, where X = O2yF3−2y, O2Cl, O2Br, and FCl2.5,7,8,27 Of these candidates, the most promising in terms of voltage range and cycling stability has been NaxV2(PO4)2F3.7 Reported substitutions on the transition metal sublattice have so far yielded inferior performance. Specifically, Na3Ti2(PO4)2F3 and Na3Fe2(PO4)2F3 have been synthesized and yielded capacities under 60 mAh/g, indicating that less than 1 sodium per formula unit could be reversibly cycled.19 Optimization of synthesis recipes and cycling conditions has led to the realization of limited additional reversible capacity via Na insertion past the synthesis composition x = 3,2 as initially predicted by Matts et al.4 Further studies have sought to improve the electrical conductivity via carbon loading with graphene,14,15 carbon nanotubes,30 and ruthenium coating.16 These strategies have all improved the cyclability of fluorophosphate cathodes with reports of 95% capacity retention after 1000 cycles at C/1016 and 50% capacity retention after 3000 cycles at 30 C.21 Similarly, nanosizing via low temperature solvothermal synthesis has led to 90% capacity retention after 1200 cycles at 10 C.17 While these optimization strategies have confirmed the promise of the fluorophosphate framework in delivering superior performance for sodium-ion batteries, to the best of our knowledge, none has achieved reversible Na extraction beyond the x = 1 limit. Achieving this goal would allow the fluorophosphate to surpass the Na-ion state-of-the-art cathode in capacity and energy density,31 and become competitive with Li-ion technologies. Clearly, the Na3V2(PO4)2O2yF3‑2y family of materials has yielded a myriad different research directions and a diverse array of experiments. Nonetheless, the puzzle of the sodium

extraction limit in these materials remains unresolved. In this report, we combine the vast body of available research with a near exhaustive computational evaluation of the structure, stability, electrochemical properties, and dynamic properties of NaxV2(PO4)2F3 to provide insight into the factors limiting the extraction of the final sodium and justification to observed but unexplained phenomena that arise during cycling.

2. METHODS We begin our study of the vanadium fluorophosphate by calculating the energy of all topologically distinct sodium orderings within the P42/mnm β-Na12V8(PO4)8F12 conventional cell (a = 9.047 Å; c = 10.705 Å)11 and identifying the ground state structures. Through full configurational enumeration at this length scale, we believe that we are able to capture all relevant sodium interactions, giving us a good estimate of the full lattice Hamiltonian for this system. We rely on the EnumLib package for structural enumeration,32−34 and the spglib package for all symmetry analysis.35 Additionally, we analyze the ground states of the Na12V8(PO4)8O4F8 and Na12V8(PO4)8O8F4 systems. For Na12V8(PO4)8O8F4, the oxygen−fluorine site occupation is known, but structural enumeration was required for Na12V8(PO4)8O4F8. Finally, we rely on the pymatgen package for the generation of input files, thermodynamic analysis, and the elimination of symmetrically equivalent structures from our data set.36−40 All calculations were performed using density functional theory, as implemented in the Vienna Ab initio Simulation Package (VASP),41−45 using projector-augmented wave (PAW)45,46 pseudopotentials with a 520 eV cutoff, and a Γ-centered k-point mesh with a reciprocal space discretization of 0.25 Å−1. We rely on the Hubbard−U corrected PBE47,48 exchange correlation functional as proposed by Dudarev et al.,49,50 with a Ueff = 3.1 eV applied to the d states of V, based on previously reported optimization for formation energies across vanadium oxide compounds.51 Note that while the voltage of the sodium fluorophosphate has been best reproduced by a slightly larger Ueff = 4.0 eV,7,27 our U value yields more reliable energies for competing phase reactions, at the cost of a constant offset on the voltage equal to 0.4 V. DFT calculations were conducted without any symmetry constraints, thereby allowing Na atoms to relax into their most stable positions, if necessary moving away from the original P42/mnm sites. To assess the dynamics of sodium in the structure and determine Na-diffusivity, we performed ab-initio molecular dynamics (AIMD) simulations under the Born−Oppenheimer approximation using VASP.43 Within these simulations, we calculate atom trajectories 5451


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Chemistry of Materials using Newtonian dynamics with Verlet integration in a NVT ensemble, relying on a Nose-Hoover thermostat with a period of 40 timesteps (80 fs) in all simulations. We calculate Na atom displacements with respect to the center of mass of the framework (non-Na) atoms and obtain self-diffusivities by fitting the Einstein relation of mean squared displacements to time (⟨||Δx||2⟩ = 2dDself t), where d is the dimensionality, using tools implemented in the pymatgen software package.36 For all AIMD simulations, we use the same conventional cell as that used for configurational enumeration, constraining the volume and shape of the cells to that obtained from a full relaxation in the ground state energy calculations. The time step of the simulation was 2 fs. To reduce the computational cost of the calculation, we calculate forces using a single k-point. We initialize all temperatures at 300 K and then scale to the appropriate temperature over 1000 time steps (2 ps), starting with the ground state structure. Finally, we calculate the activation energy (Ea) and extrapolate results to room temperature with an Arrhenius fit to the diffusivity data.

3. RESULTS AND DISCUSSION 3.1. Structural Analysis. We begin our analysis by considering the zero-temperature ground states of the NaxV2(PO4)2F3 system and resulting voltage curve as a function of sodium composition in order to both ascertain the structural evolution of the system and establish a connection between our computational model of the material and experimental studies. The convex hull obtained by calculating the energies of all possible orderings within the 4-formula unit conventional cell (16-Na supercell) is given in Figure 1a). The convex hull plot provides a representation of the thermodynamics of the systemstable phases are shown as blue points, and phases unstable with respect to the convex hull are shown as red points. The ground state structures, given in Figure 2, offer a direct comparison to experimental in situ results on the structure of the compound during reversible sodium deintercalation.20,52 In order to discuss the evolution of the sodium fluorophosphate structure, we first define the general framework of the NaxV2(PO4)2O2yF3−2y system and the various sites available for sodium. In general, the structure contains V2O8+2yF3−2y bioctahedra consisting of vanadium centers coordinated by oxygen and fluorine ions, with the fluorine occupying the sites along the z-axis of the bioctahedra. Phosphate groups connect the bioctahedra and separate the two-dimensional layers of Na-ions, which lie in the ab-plane of the cell. As the arrangement of Na-ions is primarily twodimensional, the most significant interactions guiding the energetics and dynamics of Na are those within and in-between two-dimensional rings of Na-sites, which lie between the ends of nonbonded bioctahedra. The interlayer interactions are expected to be small compared to the strong electrostatics governing the intraring interactions felt within the sodium layers. As a result, the majority of work on characterizing the structure of the fluorophosphate and proposing reaction mechanisms for its electrochemical behavior has focused on the evolution of sodium site occupancy within these twodimensional rings. Some confusion in naming arises here, as the indexing and naming conventions of these sites depend on the space group chosen to represent the structure. In general, as shown in Figure 3, Na can occupy sites lying along the [100] and [010] directions from each bioctahedron center, as well as smaller sites lying along the [110] directions from the center of the ring, for a total of 8 Na-sites per ring. Depending on assumptions made about the structure, some of these sites become degenerate or are not explicitly represented. For example, the commonly reported structure, occupying the

Figure 2. Ground state Na orderings of NaxV2(PO4)2F3, derived via enumeration of all possible Na-vacancy orderings within the unit cell shown. Layer 1 and layer 2 refer to the two Na layers in the structure. The orderings found are consistent with those observed by Bianchini et al.52,53 based on in situ characterization, with the specific ordering given for Na2V2(PO4)2F3 in agreement with experimentally derived constraints on the structure.52

P42/mnm spacegroup, does not include the diagonal [110] sites and groups adjacent [100] and [010] sites as equivalent Na(1) or Na(2) sites. The alternative Cmcm structure includes the diagonal [110] sites as Na(3) sites and defines all [010] sites as Na(1) and [100] sites as Na(2). This distinction is fundamentally related to the energetics of the various Nasites, and thus, the order and voltage of their extraction. Thus, in the following paragraphs, we aim to reconcile the various proposed structures of NaxV2(PO4)2F3, their symmetry, and Na-site energetics, and obtain a consistent interpretation of reported structural and electrochemical data. As an initial validation of our model, we confirm that the computed ground states are consistent with those proposed experimentally across all sodiation levels.52 At the synthesis composition, Na3V2(PO4)2F3 (x = 3), we find the ground state to be within the Cmc21 spacegroup with a comparable orthorhombic distortion of the a and b lattice parameters, b/a ∼ 1.004, as Bianchini et al., who report b/a ∼ 1.002.53 Computed structural parameters for Na 3 V 2 (PO 4 ) 2 F 3 , Na 3 V 2 (PO 4 ) 2 OF 2 , and Na 3 V 2 (PO 4 ) 2 O 2 F are shown in 5452


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Figure 4. Two possible NaV2(PO4)2F3 Na-vacancy orderings. The “orthorhombic” structure has been reported by Bianchini et al. and contains occupied Na(1) sites.52 The “low entropy relaxation” structure is the ground state of NaV2(PO4)2F3 within our zerotemperature calculations and has occupied Na(3) sites. This structure is stable only if full lattice relaxation is permitted because it is accompanied by a 1.3° distortion in the γ angle and is unlikely to be observed at finite temperature due to its low configurational entropy relative to the “orthorhombic” structure.

Figure 3. Schematic definition of sodium sites in Na3V2(PO4)2F3 within a single sodium layer, as well as a comparison of indexing conventions for these sites in the P42/mnm and Cmcm space groups.

Table 1. Structural Parameters Describing Na3V2(PO4)2O2yF3‑2y as a Function of Fluorine/Oxygen Concentration for y ∈ [0, 0.5, 1] a (Å) b (Å) c (Å) α (deg) β (deg) γ (deg) spacegroup b/a

y=0

y = 0.5

y=1

9.15 9.19 10.9 90 90 90 Cmc21 1.004

9.14 9.18 10.7 90.6 90 90 P21/m 1.005

9.13 9.15 10.6 90 90 90 Cmcm 1.002

At the composition NaV2(PO4)2F3, we find two low energy sodium orderings, shown in Figure 4. The “orthorhombic” structure, which we obtain as the lowest energy structure within an orthorhombic lattice, occupies the Cmcm spacegroup and is compatible with the sodium ordering of the experimentally reported structure.52 Importantly, we do not predict the experimentally reported V4+ → V3+, V5+ disproportionation.52 This charge ordering would break the Cmcm symmetry of our structure and recover the Cmc21 spacegroup reported by Bianchini et al.52 The fully relaxed, “low entropy relaxation”, structure occupying the Pm spacegroup is marginally lower in energy than the “orthorhombic” structure and has all of the Na ions occupying Na(3) sites. This lowest energy structure includes a lattice distortion in the γ angle. We find that in the “orthorhombic” structure, the Na(1) and Na(3) sites are within 30 meV of each other, indicating that at finite temperature we must expect that some disorder and occupation of the two neighboring Na(3) sites will occur. The lattice distortion required to stabilize the Na(3) sites in our zero-temperature ground state calculation does so at the expense of increasing the energy of all other sodium sites, with a corresponding entropic penalty. At finite temperatures, this effect will lead to the stabilization of the orthorhombic Cmcm structure, in line with experimental observations.52 A further complication arises due to chemical variations on the anion sublattice. On the basis of a series of overcharge studies, Palomares et al. report that in Na0.5V2(PO4)2O1.4F1.6, sodium preferentially occupies adjacent [100]/[010] sites, indexed as the Na(2) sites of the P42/mnm space group, while in Na1.2V2(PO4)2O2F1, sodium occupies the opposite [010]/ [100] site pair, indexed as the Na(1) site of the P42/mnm space group.55 Similarly, Bianchini et al. report that in NaV2(PO4)2F3, sodium occupies the [010]/[100] sites, indexed as Na(1) within P42/mnm. We compare the energies of both our predicted and the experimentally reported structures under the constraint that all lattice angles remain 90° but allowing all internal degrees of freedom to fully relax for the compositions NaV2(PO4)2O2yF3−2y, y ∈ [0, 0.5, 1]. Under the orthorhombic constraint, the [110] Na(3) sites become unfavorable with respect to the [010] Na(1) sites for y = 0 and y = 1 but remain

Table 1. While the ground state structure of Na3V2(PO4)2F3 (Figure 2) takes on a spacegroup that differs from the reported structure, this difference can be explained by considering the low-energy excited states at this composition. The eight lowest energy structures are nearly degenerate and lie within 4 meV/Na of the stable state. Accounting for thermal excitations, we can average the Na site occupations of these structures to obtain a disordered structure that is consistent with the experimentally reported Cmcm spacegroup. This result is critical to understanding the evolution of the fluorophosphate structure because, while many previous reports attribute features observed during cycling to the preferential extraction from Na(1) or Na(2) sites of the P42/mnm structure,6,8,22,24,54 the Cmcm structure contains three distinct sodium sites that offer a different interpretation of experimental results. The Na(1) and Na(2) sites in the Cmcm structure are nearly equivalent, with their degeneracy broken by the orthorhombic distortion in Na3V2(PO4)2F3. The additional Na(3) site is occupied as a relaxation of a Na-ion off a Na(1) site, as this relaxation reduces the electrostatic repulsion from the other Na-ions in the structure. Also, the Na(1) and Na(2) sites of the Cmcm spacegroup are not congruent with those of the P42/mnm group. As a result, many of the proposed mechanisms for sodium site occupancy must be re-evaluated within the framework of the Cmcm spacegroup, as we discuss in a later section. 5453


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Chemistry of Materials favorable for y = 0.5. The resolution of these structural details allows us to reconcile the results of Palomares et al. with our own model of the system. Since Palomares et al. indexed the fluorophosphate using the P42/mnm spacegroup, the [110] Na(3) sites are not considered by symmetry constraints, meaning that any [110] sites in the structure would be interpreted as off-lattice P42/mnm-Na(1) or Na(2) sites. As a result, a possible interpretation of the reported occupations is that the observed P42/mnm-Na(1) sites in the y = 1 and y = 0 compounds correspond to partially occupied [010] sites, while the off-lattice P42/mnm-Na(2) sites in the y = 0.7 compound correspond to [110] Na(3) sites. Taking this change in labeling convention into account, we confirm that our results are completely consistent with the experiment for all reported orderings across all compositions. We conclude that the [110] Na(3) sites, commonly believed to be high energy, are stabilized at specific anion and sodium compositions. One structure in this system that has eluded characterization previously is that of Na2V2(PO4)2F3 (x = 2). The ground state structure that we find at this composition is in agreement with the constraints put forth by Bianchini et al.,52 which we demonstrate schematically in Figure 2. Note that the sites marked with green circles and the sites marked with black circles are never simultaneously occupied within the same Na ring. The calculated structure occupies the Cmmm spacegroup, distinct from the Pmmm structure needed to index all of the observed diffraction peaks, as reported by Bianchini et al.52 It is likely that the true structure is composed of the same ordering in each sodium layer, with layer stackings lowering the overall symmetry. Furthermore, we are able to explain a curious feature of the Na2V2(PO4)2F3 ordering; while the occupied sodium sites at this level of sodiation are nearly structurally identical, low-temperature NMR indicates the presence of two distinct sodium environments in the structure.20 We find that this apparent contradiction can be explained by considering the charge ordering on the metal sublattice, as shown in Figure 5. At this level of sodiation, vanadium exists in the V3+ and V4+ oxidation states, analogously to the mixed oxidation states expected at the fully sodiated and fully desodiated limits. In the fully desodiated and fully sodiated limits, the vanadium charge

ordering does not break the symmetry of the Na(1) and Na(2) sites. In contrast, at x = 2, vanadium forms planes of V3+ and V4+, which creates four distinct sodium environments, shown in Figure 6, of which two are occupied: one in which the Na-ions

Figure 6. Each panel depicts a distinct Na environment within the ground-state structure of Na2V2(PO4)2F3, with the V3+/4+ charge ordering shown in Figure 5c). Following the Na−V interaction model of Park et al.,7 the Na sites with strong 90° interactions with V3+ are all occupied, and Na sites with V4+ strong interactions are vacant.

interact with four V3+ ions and a second in which the Na-ion interacts with two V3+ and two V4+ ions. These two environments can be resolved via NMR but would be difficult to distinguish by X-ray diffraction. Combined with our previous analysis of sodium sites, this elucidation of sodium environments at all states of charge allows us to proceed from the thermodynamic convex hull of the system to evaluating the evolution of this system on cycling. Following this thermodynamic characterization, it is straightforward to examine the evolution of sodium environments in the system in order to understand all features in the voltage curve of the system, as shown in Figure 1 b). While the steps in the voltage curve at x = 1 and x = 3 can be explained by changes in the active transition metal redox couple, the voltage change at x = 2 has been previously attributed to the preferential extraction of sodium from P42/mnm-Na(2) sites, followed by the extraction from the more stable P42/mnmNa(1) site. However, within the correct Cmcm structure, the [100] and [010] sites, indexed as Na(1) and Na(2), are near degenerate, and in agreement with Liu et al.,20 we do not find evidence for the preferential extraction from either the [100] or [010] sites. Instead, we find that between x = 3 and x = 2, sodium is extracted from the [110] Na(3) site, which, as discussed earlier, is occupied at x = 3 due to strong Na−Na electrostatic interactions incurred at Na3V2(PO4)2F3. The sharp change in voltage at x = 2 arises from strong Na-vacancy and V3+−V4+ orderings in the system, rather than the behavior of the active redox couples, consistent with strong Na-vacancy orderings commonly found in Na-ion battery systems.1 Finally, the voltage of the final 0 ≤ x ≤ 1 plateau, corresponding to the extraction of Na from Cmcm-Na(1) sites of NaV2(PO4)2F3 and the oxidation of V4+ to V4.5+, lies at 4.9 V, in close agreement to the previously reported 5.0 V voltage figure.7,27 3.2. Phase Stability. Having established the structure of the fluorophosphate system across its entire composition range, we move to address the issue of reversible sodium extraction limits in this material and its promise as a Na-ion cathode. A critical parameter of an intercalation material is the stability of

Figure 5. Electronic state ordering of vanadium in (a) Na4V2(PO4)2F3, (b) Na3V2(PO4)2F3, (c) Na2V2(PO4)2F3, (d) NaV2(PO4)2F3, and (e) V2(PO4)2F3. The charge ordering in Na2V2(PO4)2F3 splits the otherwise identical Na environments shown in Figure 2. These distinct environments correspond to the two distinct Na-environments previously reported from NMR.20 5454


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Ascertaining the stability of the V2(PO4)2F3 phase is critical to assess the potential for extraction of the final Na-ion. We find this phase to be unstable against decomposition into PF5 (ICSD ID: 62554), VF4 (ICSD ID: 65785), VP2O7 (ICSD ID: 93022), and VOPO4 (ICSD ID: 9413).60−62 However, the driving force for this decomposition is, once again, small (12 meV/atom) and would require a large amount of bond breaking and reformation as four distinct phases would need to form. By employing the same kinetic argument as that for Na2V2(PO4)2F3, we find that it is unlikely that V2(PO4)2F3 would decompose at any practically relevant rate.63 Further support for this conclusion is afforded by the fact that the sodium-inserted phase, Na4V2(PO4)2F3, has recently been synthesized.2 We find this sodium-rich phase to be similarly unstable against the synthesis composition Na3V2(PO4)2F3 (ICSD ID: 194603), VP (ICSD ID: 42444), V2O3 (ICSD ID: 260212), Na3VF6 (ICSD ID: 27347), and Na5V(PO4)2F2 (based on ICSD ID: 171748) by 17 meV/atom, exhibiting the same characteristics that we believe would prevent decomposition at any practically relevant rate. Thus, it is likely that NaxV2(PO4)2F3 will resist phase decomposition at all levels of sodiation, maintaining the reversibly cyclable topotactic framework necessary for long cycle life. Since the O/F sublattice composition is not fixed in this system, we have further investigated the phase stability of fluorophosphate systems with a variety of fluorine−oxygen ratios, specifically NaxV2(PO4)2OF2 and NaxV2(PO4)2O2F. For the alternative O/F compositions, we find that the fully occupied x = 4 phase becomes substantially more unstable, making topotactic sodium insertion into these compounds beyond x = 3 unlikely. We also report that the stoichiometric compositions x ≤ 3 are all within 10 meV/atom of the thermodynamic ground state (constraining the composition by the redox limitations of vanadium). Specifically, the minimal driving force for decomposition in V2(PO4)2OF2 suggests that analogously to the NaxV2(PO4)2F3 fluorophosphate, we may expect full sodium extraction to be possible based on grounds of thermodynamic stability. 3.3. Sodium Dynamics. While the fully desodiated phase appears to be attainable by purely thermodynamic arguments, its practical accessibility by sodium deintercalation is more difficult to ascertain. The first problem underlying the sodium extraction limit is the voltage required to drive the reaction beyond the x = 1 threshold. As can be seen in Figure 1, the voltage of the 0 ≤ x ≤ 1 plateau is 4.9 V, accounting for the 0.4 V offset of our calculated voltages and experimental results in the 1 ≤ x ≤ 3 regime. This voltage indicates that the final sodium extraction plateau in the vanadium fluorophosphate is indeed above the electrolyte stability limit for typical sodium electrolytes (4.5 V).28 One way to address this issue is through transition metal substitution, replacing V with a similar but lower-voltage transition metal that could reduce the extraction voltage of sodium and thereby increase the accessible capacity of the fluorophosphate compound, or anion sublattice engineering, as reported by Park et al.7 It is nonetheless likely that the high voltage associated with the final deintercalation step is only part of the reason for the limited cyclability of the fluorophosphate. On the basis of a series of in situ XRD experiments, Palomares et al. report that upon overcharge to 4.8 V, the Na3V2(PO4)2O2yF3−2y system (y ∈ [1, 0.8]) shows only limited sodium extraction that is highly dependent on the anion sublattice composition. This result is unexpected given purely thermodynamic constraints on

the metal-anion framework at various states of charge. To identify any possible decomposition pathways that may affect the sodium fluorophosphate, we evaluate the stability of NaxV2(PO4)2F3 against an internal database of computed ICSD structures and predicted compounds using methods discussed in refs 56−62. On the basis of our results, given in Table 2, we conclude that this framework is indeed likely to be Table 2. Phase Stability of NaxV2(PO4)2O2yF3‑2y. NaxV2(PO4)2F3 (y = 0) Only Exhibits a Moderate Driving Force for Decomposition at x = 4a fluorination (y) 0

0.5

1

sodiation (x)

decomposition energy (meV/atom)

decomposition products

4

17

Na3V2(PO4)2F3, VP, V2O3 Na3VF6, Na5V(PO4)2F2

3 2

0 3

1 0

0 12

4

54

3 2

0 5

1

6

0 4

1 49

3 2 1

0 0 0

NaVPO4F, Na2VF5, NaV2(PO4)3 PF5, VF4, VP2O7, VOPO4 NaVPO4F, V2O3, Na5V(PO4)2F2 NaVOPO4, Na2VF6, NaV2(PO4)3 VOPO4, Na2VF6, NaV2(PO4)3 PF5, VOF3, VOPO4 NaVOPO4, V3O5, Na5V(PO4)2F2 Na3V3(PO4)4, Na5VO(PO4)2F

a Note that the x = 0 and x = 2 structures are within 12 meV/atom of the ground state energy, indicating that the driving force for decomposition is small and likely unable to overcome the kinetic limitations due to the large amount of bond rearrangement and diffusion necessary to decompose into more than two phases. NaxV2(PO4)2OF2 (y = 0.5) is more unstable at full sodiation (x = 4), indicating that it would likely decompose, but otherwise remains only minimally unstable for x ≤ 3. Similarly, NaxV2(PO4)2O2F (y = 1) is significantly unstable on full sodium insertion (x = 4) but remains stable for x ≤ 3, with the exception that the fully desodiated x = 0 phase is inaccessible due to vanadium’s 5+ oxidation limit.

highly stable across all possible levels of sodium extraction and insertion. Foremost, both the synthesized composition Na3V2(PO4)2F3 and the typical terminal cycling composition NaV2(PO4)2F3 are stable against competing phases. The intermediate x = 2 phase, while stable against the Na3V2(PO4)2F3−NaV2(PO4)2F3 composition line, is weakly unstable against a set of three other phases in the phase diagram. However, segregating into three phases would require substantial mass transport, and with only a 3 meV/atom driving force, this decomposition is likely avoided at any practical cycling rate, explaining the high cycle life observed in the fluorophosphate material. The stability of the fluorophosphate structure is a desirable and rare trait, as few intercalation compounds are known where both the charged and discharged states are thermodynamically stable. 5455


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Figure 7. Diffusivity of Na in NaxV2(PO4)2F3 as a function of sodiation level derived from ab initio molecular dynamics. Sharp drops in the diffusivity at x = 2 and x = 3 indicate that diffusion is impeded at ordered, stoichiometric sodiation levels, suggesting that the ease of sodium migration is determined by off-stoichiometric defects.

sodium redox activity in the system, as calculated by Park et al.7 and confirmed by us, the voltage necessary for complete desodiation at this mixed anion sublattice composition lies between 4.6 and 4.7 V. The terminal Na-extracted composition of the compound is constrained by the Na concentration at which all of the vanadium is in the 5+ oxidation state, meaning that for the y = 1 sample, the terminal composition is NaV2(PO4)2O2F (x = 1) and for the y = 0.8 sample, it is Na0.6V2(PO4)2O1.6F1.4 (x = 0.6). Considering that the voltage required to reach these levels of sodiation for both anion compositions is reliably below 4.8 V, based on purely thermodynamic arguments, the terminal redox-limited V5+ sodiation level should be obtainable. While voltage-capacity curves are not provided by Palomares et al., it is reported that the y = 0.8 and y = 1 samples reach sodium compositions of x = 0.508 and x = 1.2 respectively. (The authors note that the extraction limit, as constrained by the V5+ charge state, is x = 0.6 for the reported composition and that the reported x = 0.508 is in excess of this, but do not discuss it further.) Thus, while the mixed valent, y = 0.8, structure is able to extract to the V5+ redox limit, the ordered, y = 1, structure is unable to fully exact sodium at 4.8 V overcharge. This result suggests that disorder on the anion sublattice can influence the accessibility of sodium in the structure independently of the voltage. Given that the sodium extraction limit appears to not be fully explained by the voltage of the final plateau, we proceed to examine the dynamics of sodium during cycling. Liu et al. report a precipitous drop in sodium diffusivity near x = 1,20 which is puzzling as previously reported sodium migration barriers for vanadium fluorophosphates with y ∈ [1, 0.7, 0] are between 200 and 400 meV at all levels of sodiation in the 0 ≤ x ≤ 3 range.4,6,27,64 (Here and for the remainder of this article, we refer to the diffusion activation energy as the sum of the defect formation energy and the migration barrier.) Typically, such low migration barriers would suggest sufficient alkali mobility, facilitating good cycling performance. Similarly, the fluorophosphate lattice does not undergo layer collapse upon sodium extraction, unlike the layered cathode materials.65 In order to elucidate the source of this apparent discrepancy, we have performed a series of ab initio molecular dynamics

simulations at all levels of sodiation between x = 1/4 and x = 15/4 within the anion-ordered y = 0 compound. On the basis of the diffusivity of sodium as a function of temperature, shown in Figure 7, we extract the activation energies for sodium diffusion. Noting that while sodium motion in its local “ring” environment remains facile at all levels of sodiation, these paths are nonpercolating and thus do not contribute to macroscopic diffusion. As can be seen from the AIMD-extracted diffusion activation energies given in Table 3, sodium diffusion is facile when the sodium composition differs from that of the ground state compositions but is difficult at the ground state stoichiometries. This trend suggests that the underlying cause of the drop of sodium diffusivity at x = 1 is related not to the Table 3. Activation Energy of Na Diffusion in NaxV2(PO4)2F3 as a Function of Sodiation Level Derived from ab-Initio Molecular Dynamicsa composition (NaxV2(PO4)2F3)

activation energy (meV)

uncertainty (meV)

3.75 3.50 3.25 3.00 2.75 2.50 2.25 2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25

505 635 726 811 155 183 282 556 228 211 181 353 229 383 232

92 105 124 65 40 35 35 62 46 33 35 30 64 63 36

The activation energies at the ground state compositions at x ∈ [3, 2, 1], shown in bold, are particularly large because migration at these ordered compositions requires the creation of a defect. Thus, these activation energies include the defect formation energy as well as the migration barrier.

a

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stoichiometric defects rise to over 700 meV, such that the most stable mobile defect becomes the stoichiometric sodium rearrangement at 620 meV. Naturally, at such a high formation energy, we would expect the defect population in the material to drop by several orders of magnitude, correspondingly increasing the activation energy for diffusion and lowering the sodium diffusivity. This mechanism helps explain the precipitous drop in sodium diffusivity near the x = 1 sodiation level reported by Liu et al.20 In the experiment, due to electrolyte stability limits, the voltage at which the drop in diffusivity was observed to decrease was 4.5 V, in between the x = 1 oxidation and reduction levels, where we would expect the defect formation energy and correspondingly, the activation energy for diffusion, to be maximized. The defect energetics shown in Figure 8 also allow us to compare the contribution of defect formation to the sodium diffusivity at x = 1 and x = 2. As discussed earlier, while the sodium fluorophosphate has excellent ionic conductivity at the intermediate x = 2 composition, it appears that at x = 1, diffusion plays a role in limiting the degree to which sodium can be extracted from the structure, on top of the voltage and electrolyte stability issues. Under all conditions, the energy required to form a mobile defect near the x = 2 composition is approximately 100 meV lower than at x = 1, which translates to an order of magnitude difference in room-temperature ionic diffusivity. While relatively small, this drop in diffusivity must be expected to lead to higher overpotentials required for cycling past the x = 1 sodiation level at constant current. Most importantly, we can conclude that the origin of the change in sodium diffusivity on cycling indeed lies in the defect energetics of the material rather than the migration barrier of sodium in the structure. This result suggests that these diffusion issues may be resolved by a number of strategies that could lower the defect formation energy and destabilize the sodium ordering at x = 1. One such strategy is to lower the defect formation energy by introducing disorder into the system, either through disorder on the anion sublattice or transition metal mixing. Specifically, as transition metal substitution can also decrease the voltage necessary to extract sodium from the structure to a level within the electrolyte stability window, the further addition of transition metal disorder may preclude the formation of strong sodium-vacancy orderings, aiding diffusion near the ground state compositions. An example of the effect of defect energetics on the diffusivity of a material is the behavior of the isostructural Na3Al2(PO4)2F3 compound reported by Le Meins et al. In this material, the sodium composition is intrinsically tied to the anion composition as Al is redox-constrained to its 3+ charge state. For this reason, the energy required to insert or remove a sodium ion from the structure, creating an off-stoichiometry defect, is much larger than that in the vanadium fluorophosphate at all experimentally accessible conditions. Correspondingly, the experimentally reported Na diffusion activation energy of Na3Al2(PO4)2F3, provided in Table 4, is 800 meV. Previously, this high activation energy has been attributed to the smaller volume of Na3Al2(PO4)2F3 (802 Å3/unit cell) when compared to Na3V2(PO4)2F3 (876 Å3/unit cell).3,12 However, the relevant parameter for estimating the sodium migration energy is the size of the rectangular face connecting adjacent rings since this is the face that sodium must move through to migrate, as shown schematically in Figure 9. At the transition state, the Na−O bond length is only 3% larger in the vanadium system than in the aluminum system, 2.08 Å in Na3Al2(PO4)2F3

migration barrier for sodium diffusion but to the energy required to form a mobile defect in the structure. Qualitatively, at non-ground-state compositions, where these defects are likely present in large quantities, the activation energy for sodium diffusion is given only by the sodium migration barrier. At ground state compositions (x ∈ [1, 2, 3]), the strong sodium-vacancy ordering precludes the formation of mobile defects, such that the total diffusion activation energy obtained from ab initio molecular dynamics is dominated by the defect formation energy, rather than the sodium migration barrier. To gain a more quantitative understanding of the energetics of mobile defects, we examine the low-energy sodium configurations corresponding to an inter-ring sodium migration. For the x = 1 and x = 2 compositions in the ordered y = 0 compound, we consider three classes of defects: rearrangements of Na-ions between rings that preserve stoichiometry, insertion of sodium at the equilibrium reduction voltage, and extraction of sodium at the equilibrium oxidation voltage. The energies of the off-stoichiometric defects depend on the external chemical potential of sodium, i.e., the applied voltage, which is key to understanding the evolution of defect concentration throughout sodium extraction. The lowest energy defects of each type for the x = 1 and x = 2 sodiation levels are shown in Figure 8. At both compositions, the off-

Figure 8. Comparison of the defect formation energies in NaV2(PO4)2F3 and Na2V2(PO4)2F3 for the most stable defects that allow for bulk diffusion. In the case of off-stoichiometric defects, the energies are given at the chemical potential of Na corresponding to the Na-insertion or Na-extraction equilibrium. As is clear from the defect energies, mobile defects are easier to form in Na2V2(PO4)2F3 than in NaV2(PO4)2F3, in agreement with the more facile diffusion at that sodiation level seen in experiments.20 Note that the Na1, Na2, and Na3 jump labels follow the diffusion topology naming convention established by Matts et al.4

stoichiometry defects are much more favorable than stoichiometric defects at their maximum voltage, suggesting that during equilibrium sodium extraction or insertion, these defects dominate the population of mobile defects in the structure. However, if the voltage applied is insufficient to reach the equilibrium reduction or oxidation voltage, the energy of the corresponding off-stoichiometry defect increases rapidly and may even become higher than that of a stoichiometric defect. For example, at the x = 1 composition, under a moderate voltage of 4.5 V, the formation energies of both off5457


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orderings in the material to vanadium charge orderings, helping reconcile seeming inconsistencies between NMR results reported by Liu et al.20 and XRD data. Second, we have ascertained the thermodynamic stability of the fluorophosphate-type materials against decomposition across all sodiation levels. Finally, we have investigated the origin of limited sodium cyclability beyond the current 1 ≤ x ≤ 3 sodiation regime. We have found that in addition to the high voltage needed to extract sodium past the x = 1 level, sodium extraction is limited by low sodium diffusivity near the x = 1 composition. We find that this drop in sodium diffusivity originates not from limits in the sodium migration energy as would be normally expected but from the defect formation energetics of the structure. Therefore, we conclude that the introduction of disorder on the vanadium and/or anion sublattices, via transition metal substitution and aliovalent anion doping, may help to disrupt the Na-vacancy orderings, thereby lowering both the extraction voltage of the final Na and the activation energy of sodium diffusion, potentially increasing the reversible capacity of the fluorophosphate to its theoretically predicted level.

Table 4. Compilation of Reported Na Diffusion Activation Energies in Transition-Metal Substituted Fluorophosphates of the Form Na3M2(PO4)2O2xF3‑2x, M ≠ V composition

expt/comp

activation energy (meV)

ref

Na3Al2(PO4)2F3 Na3‑δTi2(PO4)O2F Na3Ti2(PO4)2O2F

expt AIMD expt

800 480 490

10 66 67

Figure 9. Reaction coordinate of a Na3 jump as defined in ref 4. The energetic peak in the reaction coordinate occurs as the Na atom passes through the face of the adjoined Na(3) sites. The mean distance from these four oxygen atoms is a critical parameter in the estimation of the activation barrier. In Na3V2(PO4)2F3, the mean Na−O bond distance at the saddle point is 2.15 Å52 versus 2.08 Å in Na3Al2(PO4)2F3.10

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

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to 2.15 Å in Na3V2(PO4)2F3. It is unlikely that such a small structural change can account for the dramatic difference in the sodium diffusivities of these two materials. Given that our calculated AIMD activation energy in Na 3V 2 (PO 4 ) 2F 3 , 811 meV, is comparable to that of the Al analogue, a more plausible explanation is that the origin of poor sodium diffusivity in Na3Al2(PO4)2F3 lies in the high formation energy of stoichiometry-constrained defects that are needed for diffusion. By analogy to Na3V2(PO4)2F3, if we estimate this defect formation energy to be near 600 meV and the migration barrier to be approximately 300 meV, we obtain a total activation energy for sodium diffusion of 900 meV, in reasonable agreement with the reported 800 meV activation energy.10 The example of Na3Al2(PO4)2F3 demonstrates the importance of defect formation to sodium diffusivity in this framework and further supports the concept that optimization of fluorophosphate cathodes would benefit from targeting structures with low defect formation energies. Thus, we speculate that through a combination of transition metal substitution to lower the voltage of the 0 ≤ x ≤ 1 sodiation plateau and defect engineering, it is possible to design a fluorophosphate Na-ion cathode that is capable of cycling 3 Na per formula unit, bringing the performance of sodium-ion fluorophosphate cathodes in line with that achieved in state-ofthe-art lithium-ion cathodes.

ACKNOWLEDGMENTS We thank Dr. Matteo Bianchini for insightful discussions. We thank the Samsung Advanced Institute of Technology for funding this research. Computational resources were provided by the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231, and the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI1053575.

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REFERENCES

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