Article Cite This: J. Phys. Chem. C 2018, 122, 16649−16654
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Concerted Ion-Exchange Mechanism for Sodium Diffusion and Its Promotion in Na3V2(PO4)3 Framework Qiang Wang, Mingying Zhang, Chenggang Zhou,* and Yanling Chen* Faculty of Materials Science and Chemistry, China University of Geosciences Wuhan, 388 Lumo Road, Wuhan 430074, Hubei, P. R. China
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ABSTRACT: Design and development of novel cathode materials for roomtemperature sodium ion batteries is of great importance to solve the shortage of lithium resources. As a promising candidate, the Na3V2(PO4)3 cathode (NVP) exhibits stable structure and rapid Na diffusion kinetics. A detailed insight to the transportation behavior of Na+ ions in the interstitials of NVP lattice should be of great importance for understanding the ionic conductivity as well as the electrochemical performances. In this paper, we proposed three different sodium diffusion pathways, among which the concerted ion-exchange route is found to be energetically most favorable. During the migration process, Na ions at both Na(1) and Na(2) sites are engaged in the transportation. Several dopants, including Li, K, Ca, Mg, and Al, were introduced at the Na(1) site to promote the electrochemical performance of the NVP cathode. It was found that the K-doped NVP exhibits the highest voltage and lowest lattice variation during the charge/discharge process. Moreover, the Na diffusion kinetics could be intensively promoted upon K doping. Our results provide another perspective on the Na migration mechanism in the NVP lattice and suggest that K doping should be a promising solution to enhance the electrochemical performances of the NVP cathode.
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INTRODUCTION In the recent decade, room-temperature sodium ion batteries (SIBs) have become an increasing interest to serve as an alternative electrochemical energy storage device.1 Many types of electrode materials have been developed for SIBs.2,3 Among which, the NASICON family, owing to their superior ion conductivity for Na+, is an important branch of cathode materials.1 Na3V2(PO4)3, abbreviated as NVP, is a typical NASICON cathode of SIBs.4−6 In its lattice, octahedral [VO6] and tetrahedral [PO4] building blocks share corners to construct a rigid three-dimensional rhombohedral skeleton, leaving well-defined ion channels and two classes residential sites for sodium ions.7 Na(1) locates at the octahedral centers (6b) along the c-axis and Na(2) occupies the tetrahedral sites (18e) along the b-axis with the corresponding occupancies of 1 and 2/3, respectively.8 The Na ions could be completely removed in an oxidative environment9 or be fully10/partially11 substituted by Li+ through simple ion-exchange, implying the high mobility of Na+ in the NVP framework. Because of the different bonding environments, Na(2) is expected to be more easily inserted/extracted during the electrochemical process, giving a very flat voltage plateau at around 3.3 V (vs Na+/Na) that delivers a theoretical discharge capacity of 117 mA h g−1. Upon charge, Na3V2(PO4)3 would experience a two-phase transition to NaV2(PO4)3 accompanied by a moderate volume contraction where only Na(1) occupation exists.12−14 The transportation behavior of Na+ ions in the interstitials of NVP lattice is one of the most concerned properties which © 2018 American Chemical Society
determines the ion conductivity and governs the electrochemical performances. However, the Na+ diffusion kinetics in NVP still remains disputable. Experimentally, early study on Li2NaV2(PO4)3 by Goodenough and Cushing11 suggested that Na(1) ions are immobilized during the intercalation/ deintercalation of Li+ ions at Na(2) sites where a direct Na(2) site-to-site transport mechanism of Li+ was proposed, which was demonstrated by successive studies;15 however, Masquelier et al.16 deduced from single-crystal data that a zigzag diffusion scheme17 of Na(2)−Na(1)−Na(2) may be preferred. Several theoretical efforts have also been carried out to investigate the Na+ migration mechanism.18−21 Considering that the calculated bonding population of Na(1) is larger than that of Na(2), Ji and coworkers19 suggested two facile migration pathways only for Na(2), with one passing through the channels between two [PO4] tetrahedrons along the x direction (0.090 eV) and another across the vacancies between a [PO4] tetrahedron and a [VO6] octahedron along the y direction (0.118 eV). In contrast, Na(2) diffusion along the z direction would follow a curved pathway which processes a very high migration energy (2.438 eV). Such results imply that Na(2) migration along the z axis is in fact prohibited. Using the hybrid Heyd−Scuseria−Ernzerhof functional, Ohno et al.20 proposed a polaron−Na vacancy complex diffusion mechanism. Once a Na vacancy is introduced, a nearby polaron will Received: June 26, 2018 Published: July 3, 2018 16649
DOI: 10.1021/acs.jpcc.8b06120 J. Phys. Chem. C 2018, 122, 16649−16654
Article
The Journal of Physical Chemistry C
atomic charges of the systems, we employed a fast and robust algorithm based on the Bader division scheme of charge density.29,30
be formed. The migration barrier of the polaron−Na vacancy complexes along the z direction and is slightly higher than that along x or y directions (0.353 eV vs 0.513 eV), suggesting that Na+ diffusion in the NVP lattice should be three-dimensional. These theoretical efforts have depicted the migration mechanisms from different viewpoints. For either interlayer or intralayer diffusion of Na(2),19,20 the migration pathways of Na(2) through the large spaces of the hexagonal bottleneck are more or less curved. However, most studies are based on the assumption that Na(1) does not participate in the migration process. In fact, during the electrochemical process, it is hard to imagine that all of the Na(1) ions remain immobile while only Na(2) ions participate in the intercalation/deintercalation at the 3.3 V voltage window. In other words, this assumption could be unreasonable. Therefore, we anticipated that Na(1) may also engage in the ion transportation process during electrochemical charge/discharge, as experimentally proposed by Masquelier.16 Our results reveal that a concerted ionexchange route, where both Na(1) and Na(2) are involved in the migration process, is the preferred diffusion pathway. Moreover, the doping effects at the Na(1) site, including the variations of the lattice parameter, discharge potential, and Na diffusion rate, were also carefully evaluated.
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RESULTS AND DISCUSSIONS Figure 1 shows the optimized structure of Na3V2(PO4)3 (hereafter, denoted as Na3VP). The backbone of a Na3VP
Figure 1. Optimized structure of Na3VP.
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COMPUTATIONAL DETAILS The NVP structure containing 120 atoms (18 Na, 12 V, 18 P, and 72 O atoms) is initially taken from the standard crystal data base of CCSD, followed by full optimization including the cell parameters. Similar procedures were conducted for the metal-doped NVP, where one Na atom at the Na(1) site is replaced by the dopant. The voltage during the charge/ discharge process is defined by V=
E(Na3VP) − E(Na1VP) − 2E(Na) 2e
crystal is composed of [PO4] tetrahedral and [VO6] octahedral with vertex O atoms being shared. The Na atoms are uniformly distributed in the interspace of the skeleton frame, as shown in Figure 1 where Na(1) and Na(2) are separately marked. Most studies assume that Na(2) ions are responsible for the intercalation/deintercalation during the redox around the electrochemical windows of 3.3 V, whereas the Na(1) site largely serves as a spectator that does not participate in the electrochemical reactions.15,18−21 In fact, the calculated average Na−O distance at the Na(1) site of 2.378 Å is much shorter than that at the Na(2) site of 2.521 Å, indicating that the Na(1) site is more stable than the Na(2) site. When the Na3VP is charged, only the Na atoms at Na(2) sites could be deintercalated from the lattice, leading to the formation of Na1V2(PO4)3 (hereafter, denoted as Na1VP). The structure of Na1VP is virtually identical to that of Na3VP, except a slight decrement of lattice parameters (Figure S1). According to eq 1, the calculated charge/discharge voltage of NVP is 3.23 V, in reasonable agreement of experimental value of 3.3 V. Bader charge analysis reveals that the charge/discharge voltage is largely attributed to the redox couple of V3+/V4+ with the calculated charges of +1.755e and +1.946e, respectively. To understand the mobility of Na atoms in the NVP lattice, NEB calculations were performed for Na atoms along various prescribed diffusion pathways. We first consider the possibility that a Na(1) atom migrates to an adjacent Na(2) site to partially enable its activity during the electrochemical reactions. Because the Na(2) site is more active than the Na(1) site, we rationally assume that Na ions at the Na(1) site would not migrate to the Na(2) site unless all Na ions at Na(2) sites have been deintercalated from the cathode. The structures and energies of initial, transition, and final states along this migration path are shown in Figure 2. Initially, Na+ is located at the gap between two [VO6] octahedral with an average Na−O distance of 2.378 Å. Successively, Na+ passes through a triangle consisting of three O atoms to the Na(2) site. As a consequence, the average Na−O distance decreases to 2.327 Å at the transition state and increases to 2.450 Å at the final state. Obviously, the elongated Na−O distance at the
(1)
where E(Na3VP), E(Na1VP), and E(Na) represent the total energies (in eV unit) of Na3V2(PO4)3, Na1V2(PO4)3, and an Na atom in Na bulk, respectively. 2e in the denominator stands for the total charge transfer during the redox process. Transition-state search was carried out to determine the Na migration pathways in the lattice. Typically, six intermediate images were generated based on the optimized reactant and product structures to describe the reaction pathway. Subsequently, the nudged-elastic-band (NEB) method was utilized to locate the structure of the transition state and to evaluate the activation energy along the reaction path.22 The first-principles calculations were performed using a periodic density functional theory (DFT) method implemented in the Vienna ab initio simulation package.23,24 The exchange−correlation functional proposed by Perdew, Burke, and Ernzerhof with the spin-polarization scheme was employed to calculate the electronic structures.25 The valence electrons were treated with a plane-wave basis set with a cutoff energy of 400 eV, whereas the core electrons were represented using the projector augmented wave method.26,27 The Brillouin zone integration was sampled within a 3 × 3 × 2 Monkhorst−Pack k-point mesh.28 Structure optimizations were conducted until the total energy was converged to 10−3 eV. The calculated cell parameters of Na3V2(PO4)3 (a = b = 8.667 Å, c = 21.677 Å) are in good agreement with its experimental values (a = b = 8.680 Å, c = 21.710 Å), suggesting that the above settings are accurate enough to achieve reasonable results. To calculate 16650
DOI: 10.1021/acs.jpcc.8b06120 J. Phys. Chem. C 2018, 122, 16649−16654
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The Journal of Physical Chemistry C
Figure 3. Sketch map of the direct diffusion route (path A) and stepwise ion-exchange route (path B) for Na migration. (a) Top view and (b) side view. The green and violet balls represent the Na atoms initially located at Na(1) and Na(2) site, respectively.
Figure 2. Structures (a) and energy profile (b) along the migration path from Na(1) to Na(2) site.
final state reveals that the Na−O attraction should be significantly weakened, which is detrimental to the stability of the cathode. Indeed, the migration from Na(1) to Na(2) is strongly endothermic with the calculated reaction energy of 23.8 kcal/mol. Kinetically, this process is also energetically unfavorable with a relatively high activation barrier of 36.1 kcal/mol. Our results suggest that the direction migration from Na(1) to Na(2) is essentially forbidden, in line with experimental observations.13 Now, we focus on the diffusion mechanism of Na+ at the Na(2) site migrating to a neighboring Na(2) site in the Na1VP lattice. As shown in Figure 3, two possible pathways, the direct migration route (denoted as path A) and the stepwise ionexchange route (denoted as path B), were examined. For path A, the Na(2) ion would directly pass through the small interval space between two [VO6] octahedrons and three [PO4] tetrahedrons, whereas the Na(1) ions only serve as a spectator. At the initial state, the Na(2) ion is stabilized by the surrounding O atoms with an average Na−O distance of 2.498 Å. Because the Na(2) ion is confined to a very small space at the transition state, the Na−O distance is significantly compressed to 2.106 Å, which could lead to intensive structural tension. As a consequence, the migration process needs to overcome a very high activation barrier of 63.22 kcal/ mol, indicating that Na(2) diffusion along path A is virtually kinetically forbidden (Figure 4a). Alternatively, Na(2) could follow an ion-exchange route, which is divided into two sequential steps (Figure 3, path B). At step 1, one nearby Na(1) ion moves to the final position of Na(2) and forms a Na(1) vacancy, which is then occupied by the adjacent Na(2) ion from the initial Na(2) site (step 2). Because the two steps are essentially opposite to each other, we only describe the results of the first reaction step (Figure 3, path B step 1). In this step, the Na(1) ion undergoes a similar transition state of Figure 2, where the average Na−O distance gradually decreases from 2.390 Å at the initial state (R) to 2.344 Å at
Figure 4. Calculated energy profiles along the two reaction pathways. (a) Path A and (b) path B.
the transition state (TS1), which is then elongated to 2.462 Å at the intermediate state (IM). Comparing with the results in 16651
DOI: 10.1021/acs.jpcc.8b06120 J. Phys. Chem. C 2018, 122, 16649−16654
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The Journal of Physical Chemistry C
dominative pathway for Na ion migration in the NVP lattice during the charge/discharge process, which definitely suggests that Na(1) should participate in the ionic transportation with favorable kinetics. To consider how Na(1) doping affects the electrochemical behavior, we now consider replacing one Na ion at the Na(1) site with a series of metal ions, including Li, K, Mg, Ca, and Al, to tune the lattice parameter and discharge voltage of NVP. Figure 6 shows the calculated discharge voltages and cell
Figure 2, the transition-state structure of path B has a slightly longer Na−O distance, implying that the structure tension should be delicate. Indeed, although the Na(2) atom is not directly involved in step 1, the calculated activation energy of 31.4 kcal/mol is much lower than the value in Figure 2b. In step 2, the Na(2) atom at the initial position would diffuse to the Na(1) vacancy generated in step 1 to accomplish the migration process. Comparing with step 1, step 2 is energetically more favorable with the calculated activation barrier of 14.0 kcal/mol and thermodynamic energy of −16.7 kcal/mol. Figure 4b distinctively displays that the two isolated steps of path B are in fact kinetically unfavorable; however, we mention that the thermodynamic energies are capable of compensating each other. Therefore, we rationally assume that the two sequential diffusion steps of path B might occur concertedly. To avoid misunderstanding, we here define the concerted ionexchange route as path C. The optimized initial, transition, and final structures along path C and the relevant energies are displayed in Figure 5a. To proceed the migration, each of the
Figure 6. Calculated voltage (a), c values (b), and Δc during charge/ discharge cycles (c) of NVP with various dopants.
parameters upon various dopings. The discharge voltage is highly sensitive to the dopants, which varies from 3.08 to 3.28 V. Compared with the pristine NVP, doping with the alkali metals (i.e., Li and K) would slightly increase the discharge voltage, however, which would decrease significantly when the multivalence metals are employed as doping species (i.e., Mg, Ca, and Al). Bader charge analysis shows that the excessive electrons on the multivalence metals would partially reduce the V3+/V4+ redox couple (Table 1) leading to voltage drop. For cathode materials, the higher voltage means higher energy density. Therefore, we suggest that multivalence metals are detrimental to NVP cathodes.
Figure 5. Calculated structures (a) and energy profiles (b) along the concerted ion-exchange route (path C). The green and violet balls represent the Na atoms initially located at Na(1) and Na(2) site, respectively.
two involving Na atoms need to penetrate a triangle gate formed by surrounding O atoms. Because the initial and final structures are totally same as those in path B, we only focus on the geometrics of the transition state, where each Na atom is just located in the center of the triangle gate with the same averaged Na−O distance of 2.253 Å. Such a short Na−O distance is expected to result in strong structural tension, which would increase the activation barrier. On the other hand, the distance between the two involving [VO6] octahedrons is increased from 6.202 to 6.245 Å to accommodate the structure tension. As a result, the calculated kinetic energy of 12.8 kcal/ mol is significantly lower than the value of path B. On the basis of the above results, we could rationally conclude that the concerted ion-exchange route (path C) should be the
Table 1. Calculated Bader Charges on V Atoms Na1VP (V4+) Na3VP (V3+)
Na
Li
K
Ca
Mg
Al
1.948 1.753
1.946 1.755
1.948 1.757
1.934 1.733
1.932 1.731
1.918 1.709
In addition to the voltage, the doped atoms can also change the cell parameters of the NVP. Figure 6b summarizes the optimized c values of the NVP lattice upon doping. According to the literature, the length of the c axis is a key parameter that determines the mobility of Na ions in the NVP lattice. It is believed that an elongated c axis could evidently promote the diffusion of Na.31 As shown in Figure 6b, the calculated c values fluctuate in a very small range from 21.6 to 21.7 Å, 16652
DOI: 10.1021/acs.jpcc.8b06120 J. Phys. Chem. C 2018, 122, 16649−16654
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observations.31 As a consequence, an appropriate doping rate of K is very critical to the electrochemical performance of the NVP cathode and should be carefully identified in experimental studies.
implying that the doping process would not intensively change the framework of the NVP lattice. For the alkali metals, the c values are proportional to the atom size. In contrast, the multivalence metals always result in small c values because of the strong coulombic attraction between the doping metals and the backbone O atoms. As shown in Figure 6c, the NVP lattice would also change its cell parameters to accommodate the intercalation/deintercalation of Na ions during charge and discharge cycles. Only a very small variation (
