Concerted Ion-Exchange Mechanism for Sodium Diffusion and Its

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C: Energy Conversion and Storage; Energy and Charge Transport

A Concerted Ion Exchange Mechanism for Sodium Diffusion and Its Promotion in NaV(PO) Framework 3

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Qiang Wang, Mingying Zhang, Chenggang Zhou, and YanLing Chen J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b06120 • Publication Date (Web): 03 Jul 2018 Downloaded from http://pubs.acs.org on July 10, 2018

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The Journal of Physical Chemistry

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A Concerted Ion Exchange Mechanism for Sodium Diffusion and Its Promotion in Na3V2(PO4)3 Framework Qiang Wang, Mingying Zhang, Chenggang Zhou*, Yanling Chen* Faculty of Materials Science and Chemistry, China University of Geosciences Wuhan, 388 Lumo road, Wuhan 430074, Hubei, China P.R.

Abstract Design and development of novel cathode materials for room-temperature 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, Al, were introduced at Na(1) site to promote the electrochemical performance of 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 NVP lattice and suggest that K doping should be a promising solution to enhance the electrochemical performances of NVP cathode.

Introduction In the recent decade, room-temperature sodium ion batteries (SIBs) have become an increasing interest to serve as an alternative electrochemical energy storage device1. Many types of electrode materials have been developed for SIBs2, 3. Among which, the NASICON family, owning to their superior ion conductivity for Na+, is an important branch of cathode materials1. Na3V2(PO4)3, abbreviated as NVP, is a typical NASICON cathode of SIBs4-6. 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 ions7. Na(1) locates at the octahedral centers (6b) along the c-axis and Na(2) occupies the tetrahedral sites (18e) along b-axis with the corresponding occupancies of 1 and 2/3, respectively8. The Na ions could be completed removed in oxidative environment9 or be fully10/partially11 substituted by Li+ through simple ion-exchange, implying the high mobility of Na+ in the NVP framework. Due to the different bonding environments, Na(2) are expected to be more easily inserted/extracted during electrochemical process, giving a very flat voltage plateau at around 3.3 V (vs. Na+/Na) which delivers a theoretical discharge capacity of 117 mAh 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 exist12-14. The transportation behavior of Na+ ions in the interstitials of NVP lattice is one of the most concerned properties which determines the ion conductivity and governs the electrochemical performances. However, the Na+ diffusion kinetics in NVP still remains disputable.

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Experimentally, early study on Li2NaV2(PO4)3 by Goodenough et al11 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 were demonstrated by successive studies15; however, Masquelier et al16 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 mechanism18-21. Considering 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 passes through the channels between two [PO4] tetrahedrons along x direction (0.090 eV) and another across the vacancies between a [PO4] tetrahedron and a [VO6] octahedron along y direction (0.118 eV). In contrast, Na(2) diffusion along z directions would follow a curved pathway which processes a very high migration energy (2.438 eV). Such results imply that Na(2) migration along z axis is in fact prohibited. Using the hybrid Heyd-Scuseria-Ernzerhof functional, Ohno et al20 proposed a polaron-Na vacancy complex diffusion mechanism. Once a Na vacancy is introduced, a nearby polaron will be formed. The migration barrier of the polaron-Na vacancy complexes along z direction is slightly higher than 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 inter-layer or intra-layer 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 the Na(1) ions remain immobile while only Na(2) ions participate in the intercalation/deintercalation at the 3.3V 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 Masquelier16. Our results reveal that a concerted ion exchange route, where both Na(1) and Na(2) are involved in the migration process, is the preferred diffusion pathway. Moreover, the doping effects at Na(1) site, including the variations of lattice parameter, discharge potential as well as Na diffusion rate, were also carefully evaluated.

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 fully optimization including the cell parameters. Similar procedures were conducted for the metal doped NVP, where one Na atom at Na(1) site is replaced by the dopant. The voltage during the charge/discharge process is defined by: V=

E ( Na3VP ) − E ( Na1VP) − 2 E ( Na ) 2e

(Eq. 1)

where E(Na3VP), E(Na1VP) and E(Na) represent the total energies (in eV unit) of Na3V2(PO4)3, Na1V2(PO4)3 and Na atom in Na bulk respectively. The 2e in the denominator stands for the total


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charge transfer during the redox process. Transition state search was carried out to determine the Na migration pathways in the lattice. Typically, 6 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 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 (VASP).23, 24 The exchange-correlation functional proposed by Perdew, Burke and Ernzerhof (PBE) 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, while the core electrons were represented using the projector augmented wave (PAW) 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 atomic charges of the systems, we employed a fast and robust algorithm based on the Bader division scheme of charge density.29, 30 Results and discussions Figure 1 shows the optimized structure of Na3V2(PO4)3 (here after, denoted as Na3VP). The backbone of Na3VP 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 skeleton frame, as shown in Fig. 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 3.3V, while the Na(1) site is largely serve as spectator that do not participate in the electrochemical reactions15, 18-21. In fact, the calculated average Na-O distance at Na(1) site of 2.378 Å is much shorter than that at Na(2) site of 2.521 Å, indicating that Na(1) site is more stable than 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 (here after, denoted as Na1VP). The structure Na1VP is virtually identical to 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 +1.755 e and +1.946 e, respectively.



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Figure 1. The optimized structure of Na3VP. To understand the mobility of Na atoms in NVP lattice, NEB calculations were performed for Na atoms along various prescribed diffusion pathways. We first consider the possibility that a Na(1) atom migrate to an adjacent Na(2) site to partially enable its activity during the electrochemical reactions. Since Na(2) site is more active than Na(1) site, we rationally assume that Na ions at Na(1) site would not migrate to 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 is shown in Figure 2. Initially, the Na+ located at the gap between two [VO6] octahedral with an average Na-O distance of 2.378 Å. Successively, the Na+ passes through a triangle consisting of tree O atoms to the Na(2) site. As a consequence, the average Na-O distance decreases to 2.327 Å at transition state and increases to 2.450 Å at final state. Obviously, the elongated Na-O distance at 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 observations13.

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Figure 2. The structures (a) and energy profile (b) along the migration path from Na(1) to Na(2) site.


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Now, we focus on the diffusion mechanism of Na+ at Na(2) site migrate to a neighboring Na(2) site in the Na1VP lattice. As shown in Fig. 3, two possible pathways, the direct migration route (denoted as path A) and the stepwise ion exchange route (denoted as path B), were exanimated. For path A, the Na(2) ion would directly pass through the small interval space consisted with two [VO6] octahedrons and three [PO4] tetrahedrons, while the Na(1) ion only serve as 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. Since 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 need 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, the Na(2) could follow an ion exchange route, which is divided into two sequential steps (Figure 3, path B). At step1, one nearby Na(1) 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 (step2). Since the two steps are essentially opposite to each other, we only describe the results of the first reaction step (Figure 3, path B step1). 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 the transition state (TS1), which is then elongated to 2.462 Å at the intermediate state (IM). Comparing with the results in Figure 2, the transition state structure of path B has a slightly longer Na-O distance, implying the structure tension should be delicate. Indeed, although the Na(2) atom is not directly involved in the step1, the calculated activation energy of 31.4 kcal/mol is much lowered 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, the step 2 is energetically more favorable with the calculated activation barrier of 14.0 kcal/mol and thermodynamic energy of -16.7 kcal/mol.



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Figure 3. Sketch map of the direct diffusion route (path A) and stepwise ion exchange route (path B) for Na migration. (a) top view, (b) side view. Green and violet balls represent the Na atoms initially located at Na(1) and Na(2) site, respectively.

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Figure 4. The calculated energy profiles along the two reaction pathways. (a) path A, (b) path B.


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Figure 5. The calculated structures (a) and energy profiles (b) along the concerted ion exchange route (path C). Green and violet balls represent the Na atoms initially located at Na(1) and Na(2) site, respectively. 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 ion exchange 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 two involving Na atoms needs to penetrate a triangle gate formed by surrounding O atoms. Since the initial and final structures are totally same as path B, we only focus on the geometrics of 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 kinetical energy of 12.8 kcal/mol is significantly lower than the value of path B. Based on the above results, we could rationally conclude that the concerted ion exchange route (path C) should be the dominative pathway for Na ion migration in the NVP lattice during 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 Na(1) site with a series 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 parameters upon various doping. 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).



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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 cathode.

Figure 6. The calculated voltage (a), c values (b) and ∆c during charge/discharge cycles (c) of NVP with various dopants. Table 1. The calculated Bader charges on V atoms. Na1VP (V4+) Na3VP (V3+)

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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 NVP lattice upon doping. According to the literature, the length of c axis is a key parameter that determines the mobility of Na ions in 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, 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 due to 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 (< 0.5 Å) is observed for all the involved NVP cathodes, implying that the framework should be highly stable. It is worth noting that doping with K leads to the highest c values and lowest lattice variation during charge/discharge process. Considering the highest discharge voltage upon K doping, we therefore suggest that the K doped NVP (denoted as KNVP here after) should be a promising candidate of cathode materials, in well agreement with experimental observations 31.


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In order to reduce the computational consumption, we will only focus on the Na mobility in KNVP lattice to evaluate rate performance of the cathode. Similar to NVP, we only consider the concerted ion exchange route, which is energetically more favorable, for the KNVP system. Since the size of K atom is much larger than Na atom, we assume that the K atom at Na(1) site would not directly participate the ion exchange process. Indeed, when K is involved in the diffusion process, the Na transportation becomes moderately endothermic with the calculated reaction energy of 15.6 kcal/mol. Kinetically, the K diffusion needs to overcome a relatively high activation barrier of 23.4 kcal/mol, suggesting that K migration is energetically unfavorable in KNVP lattice. In contrast, a much facile diffusion kinetics could be achieved when the K is not directly participated in the migration process. Comparing with pristine NVP, the activation barrier of Na diffusion is slightly decreased to 11.7 kcal/mol due to a slightly elongated c value of KNVP, which lowers the repulsion between Na and O at transition state and facilitates Na transportation (Figure S2). According to transition state theory, such a small decrement on activation barrier would also result in significant changes in the rate coefficient of the diffusion process. Figure S3 shows the calculated rate coefficient of Na transportation in NVP and KNVP lattice in the temperature range of -40 to 60 oC. Clearly, KNVP exhibits much higher diffusion rate than NVP in all the involved temperatures. In particular, the calculated rate coefficient of the diffusion process in KNVP is about 5.5 times higher than in NVP at room temperature (300 K), indicating that KNVP might deliver much higher rate performance than NVP. In fact, a recent experimental study also suggests that K doped NVP exhibit superior electrochemical performances.31 However, the experimental results also suggest that a higher doping rate of K is detrimental to rate performance of NVP cathode. We therefore consider to increase the doping rate of our model to address this issue. According to our model, the doping rate of KNVP is 5.6%. When an additional Na(a) site is substituted by K, the doping rate increases to 11.2% (denoted as KNVP2). It was found that a higher doping rate of K leads to negligible expansion of lattice parameters (the length of c value increases from 21.69 Å of KNVP to 21.70 Å of KNVP2). Moreover, the discharge voltage of KNVP2 (3.277 V) is also virtually identical to KNVP (3.271 V). However, the Na transportation kinetics of KNVP2 becomes unfavorable with the calculated diffusion barrier of 15.5 kcal/mol, in line with the experimental observations31. As a consequence, an appropriate doping rate of K is very critical to the electrochemical performance of NVP cathode and should be carefully identified in experimental studies.

Conclusion In summary, a series DFT simulations were conducted on the NVP to evaluate the electrochemical behaviors of the cathode. Two possible occupation sites (Na(1) and Na(2)) for Na ions were evaluated, where the Na(1) site is energetically more favorable than Na(2) site. As a consequence, only the Na ions at Na(2) sites are electrochemically active during the charge/discharge process. Three possible diffusion pathways for Na ions were then considered to address the mobility of Na ions. It was found that the preferred diffusion pathway is the concerted ion exchange route, where both Na(1) and Na(2) ions are involved in the migration process. Doping on the Na(1) site would result in changes on the lattice parameters and discharge potentials of NVP. Among all the involved dopants, the K doped NVP exhibits the highest voltage and lowest lattice variation during the charge/discharge process. Moreover, the Na diffusion velocity could be also intensively promoted in NVP lattice upon K doping. Our results provide useful insights on the Na migration



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mechanism in NVP lattice and suggest that K doping should be a promising solution to enhance the electrochemical performances of NVP cathode.

Acknowledgement. This work was supported by the Fundamental Research Founds for National University, China University of Geosciences Wuhan (Innovative Team, Grant CUG120115; “Yaolan” plan, Grant CUGL150414 and CUGL140413), the Natural Science Foundation of Hubei (2013CFB413), and the National Natural Science Foundation of China (No. 21773217). Support from the high-performance computing platform of China University of Geosciences is also gratefully acknowledged. References 1.

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