K on FeF 3

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Atomic-scale Dynamics and Storage Performance of Na/ K on FeF3 Nanosheet Shu Zhao, Yang Li, Zhenhua Yang, Xianyou Wang, and Xing-Qiang Shi ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.9b03077 • Publication Date (Web): 19 Apr 2019 Downloaded from http://pubs.acs.org on April 19, 2019

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ACS Applied Materials & Interfaces

Atomic-scale Dynamics and Storage Performance of Na/ K on FeF3 Nanosheet Shu Zhao,†,‡ Yang Li,†,‡ Zhenhua Yang,†,‡, Xianyou Wang,§ Xingqiang Shi┴,* Key Laboratory of Materials Design and Preparation Technology of Hunan Province,

†

School of Materials Science and Engineering, Xiangtan University, Xiangtan 411105, Hunan, China Key Laboratory of Low Dimensional Materials & Application Technology (Ministry

‡

of Education), School of Materials Science and Engineering, Xiangtan University, Xiangtan 411105, Hunan, China National Local Joint Engineering Laboratory for Key Materials of New Energy

§

Storage Battery, National Base for International Science & Technology Cooperation, Hunan Province Key Laboratory of Electrochemical Energy Storage & Conversion, School of Chemistry, Xiangtan University, Xiangtan 411105, Hunan, China Department of Physics, Southern University of Science and Technology, Shenzhen

┴

518055, China



Corresponding authors. Address: Key Laboratory of Materials Design and Preparation

Technology of Hunan Province, School of Materials Science and Engineering, Xiangtan University, Xiangtan 411105, Hunan, China. E-mail addresses: [email protected] (Zhenhua Yang); [email protected] (Xingqiang Shi). 1 / 36

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ABSTRACT: Developing highly efficient FeF3-based cathode materials for Na/K-ion batteries is greatly needed, which needs long cycling life and rate performance besides for large voltage and capacity. Accordingly, we designed two-dimensional (2D) FeF3 nanosheet to obtain highly efficient Na/K-ion batteries. And first-principles calculations were implemented to discuss systematically Na and K storage mechanism on FeF3 (012) nanosheet. The adsorption energies of Na and K are -3.55 eV and -3.98 eV, respectively, which can guarantee Na/K loading process. Interestingly, Na and K adatoms on FeF3 (012) prefer to get together in the form of Na dimer and K tetramer, respectively. Energy barriers of K tetramer is lower than that of Na dimer( 0.43 eV vs. 0.45 eV). As a result, K tetramer possesses larger diffusion coefficient than Na dimer (4.22×10-10 cm2·s-1 vs. 3.32×10-10 cm2·s-1). That is to say, good Na/K-ion mobility can be achieved. And FeF3 (012) nanosheet exhibits high initial discharge voltage (4.10 V for K and 3.74 V for Na). Moreover, it has stable discharge voltage curve in Na/K-ion batteries. Besides, FeF3 (012) nanosheet is more favorable to be fabricated as a flexible cathode material for potassium batteries. Therefore, 2D FeF3 nanosheet belongs to a promising cathode material in Na/K-ion batteries. KEYWORDS: Na/K ion batteries, first-principles calculations, FeF3 (012) nanosheet, cycling life, rate performance 1. INTRODUCTION For the past decades, Li-ion batteries(LIBs) have been widely applied in military, electrical vehicles and portable electronic equipments owing to their attractive energy 2 / 36


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density and wide voltage window.1-4 However, security and cost issues have restricted their development, especially in the area of large-scale energy storage.5 With the gradual emphasis on the continuous loss of global lithium reserves, metal-ion batteries need inexpensive and resource-rich materials.6 Due to advantages of sodium and potassium, such as low cost, suitable redox potential and similar physicochemical properties with lithium, LIBs are most likely to be replaced by Na-ion batteries (NIBs) or K-ion batteries (KIBs).7,8 Among many components of NIBs or KIBs, cathode materials play a key role in developing batteries with excellent electrochemical properties. Recently, transition metal fluorides,9-14 such as BiF3,11 CuF2,12 CoF213 and FeF3,14 have become an attracting

topic.

Firstly,

transition

metal

fluorides

usually

take

intercalation/deintercalation and conversion reaction with Na/K metal, which contributes to high capacity.15 Besides, strong ionic bond between transition metal ion and fluorion contributes to high voltage.16,17 As compared to other metal fluorides, FeF3 exhibits apparent advantages, such as low cost and environmental friendliness. Most of all, it can offer considerable electrode potential (4.50 V vs. Na+/Na)18 and capacity (197 mAh/g).19 On the other hand, due to the lower standard potential of K+/K than that of Na+/Na (-2.88 V vs. -2.56 V),20 higher voltage can be obtained in KIBs relative to NIBs. Unfortunately, poor electronic conductivity of FeF3 can scarcely be improved radically in the short run , which results in poor cycling life and rate performance of NIBs or KIBs.21 In order to improve electrochemical properties of FeF3, great efforts have been made in recent years, such as ionic doping to decrease its 3 / 36



band gap,22,23 surface coating with conductive agent to improve electronic conductivity24,25 and fabricating nanocomposites to shorten both electronic and ionic pathways.26 Although the electrochemical properties of FeF3 have been improved in a way, its cycling life and rate performance are still unsatisfactory. Hence, a new strategy to solve these problems become urgent. Fortunately, rapid development of two-dimensional (2D) materials affords a new approach to solve bottleneck of FeF3 in recent years.27 2D materials as an emerging class of nanoscale materials show unprecedented properties compared to their corresponding bulk materials because they can provide higher chemically active interfaces.28,29 To date, 2D NIBs cathodes, such as oxides and transition metal fluorides,30-32 have all been reported in experiments. For example, thin V2O5 layer hold higher energy density than bulk V2O5(45.0 W·h·kg-1 vs.11.6 W·h·kg-1).30,31 NaFeF3 nanoplates shows higher initial discharge capacity than bulk FeF3 (153 mAh/g vs.120 mAh/g).27,32 Furthermore, it is noted worthy that sheet-like FeF3 exhibits better electrochemical properties, such as higher capacity, longer cycling life and higher-rate performance than bulk FeF3 when it is aced as cathode material for NIBs in recent experiment.33 Then, FeF3 (012) plane has been observed in experiment.34. Two neighbouring FeF3 (012) planes constitute ion diffusion channels.35 Besides, lithium storage mechanism of FeF3 (012) nanosheet has been theoretically investigated.36 Based on the above discussions, it is proposed that FeF3 (012) nanosheet can exhibits excellent electrochemical properties in NIBs and KIBs. However, the physical and chemical mechanisms of Na/K on the FeF3 (012) nanosheet are still unclear. Thus, how to reveal inner laws of Na/K at a micro level is 4 / 36


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critical. Due to complexity and instantaneity, it is usually difficult to describe atomic-scale dynamics and electrochemical behavior of Na/K on the FeF3 nanosheet by experiment. Therefore, we have performed first-principles calculations to explore the adsorption behavior, diffusion kinetics, mechanical properties and electrochemical properties of Na/K on the the FeF3 (012) nanosheet. 2. COMPUTATIONAL METHODS First-principles calculations were performed by utilizing VASP package with GGA -PBE potential.37,38 And PAW method was carried out to describe core electrons.38 Fe (3d74s1), F (2s22p5), Na (2p63s1) and K (3s23p64s1) were taken into account as valence electron configurations, respectively. An energy cutoff of 500 eV and k-points of 4 × 4 × 1 grids were employed. A vacuum thickness of 10 Å was built to avert interactions between FeF3 (012) nanosheet and its periodic layer. Relaxation of all structures were executed until the interaction force between atoms was less than 0.03 eV/Å. GGA+U method was employed to treat Fe 3d orbits. Here,effective interaction parameter (U-J) is equal to 5.0 eV.35 Besides, spin polarization were consdered. Na/K ion diffusion across the FeF3 (012) nanosheet were explored via CI-NEB method.39-40 And the diffusion coefficients (D) can be expressed as:

D  d 2 0 exp(

Ea ) kBT

(1)

where d, Ea ,T, kB and ν0 are the hopping distance of Na/K, energy barrier, Boltzmann constant, temperature and attempt frequency ( 1013 Hz),41 respectively.

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3. RESULTS AND DISCUSSION 3.1 Na/K Adsorption on the FeF3 (012) Nanosheet FeF3 possesses a hexagonal crystal structure with R3C

space group and the

lattice constants are: a = 5.198 Å, c = 13.330 Å.42 Recently, it is found that F-termination exhibits good stablilty with regard to different terminations of FeF3 (012).36 Therefore, we turned to investigate Na/K adsorption behavior on the F-terminated FeF3 (012). Preferred sites for Na/K adsorption were explored. As shown in Figure 1a,b, from the symmetry analysis, five typical Na/K adsorption sites were discussed: (1) sites above the first layer of F atoms (T-site); (2) the hollow site between F1 and F2 atoms (B-site); (3) the hollow site between F1 and F3 atoms (B1-site); (4) the hollow site among F1, F2 and F4 atoms (H-site); (5) the hollow site among F1, F3 and F4 atoms (H1-site). Adsorption energy (

Ads

) is calculated to

assess the stability of these five atomic configurations. And it can be defined as:

EAds = Eabsorbed state - (Eabsorbent + Esubstrate )

(2)

where Eabsorbed state represents total energy of FeF3 (012) nanosheet with Na/K atom, Eadsorbent and Esubstrate are the total energies of Na/K atom and FeF3 (012) nanosheet, respectively. Na and K adatoms both prefer to occupy the H-site. And their adsorption energies are -3.55 eV and -3.98 eV, respectively. Besides, we further obtained the cohesive energies of the bulk Na and K according to the method in our recent work36 (-1.08 eV for Na and -0.87 eV for K), which are agree with the experimental values ( -1.11 eV for Na and -0.87 eV for K ).43 Hence, quick loading 6 / 36


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process of both Na/K ions on the FeF3 (012) nanosheet can be ensured. To the best of our knowledge, there must be strong binding of the metal atoms with electrode materials.40 Hence, FeF3 (012) nanosheet meet the requirement in this respect. Next, we further reveal the adsorption mechanism of Na/K on the FeF3 (012) nanosheet via charge density difference (ρAds ) and it can be determined by: ρAds = ρabsorbed state - (ρabsorbent + ρsubstrate)

(3)

where ρabsorbed state is the charge density of FeF3 (012) nanosheet with Na/K atom, ρabsorbent and ρsubstrate indicate the charge density of Na/K atom and the charge density of FeF3 (012) nanosheet, respectively. Charge density difference of Na and K-occupation at H-site are shown in Figure 1c and Figure 1d, respectively. Evidently, charged-depleted regions appear around the Na/K atoms, which suggests that charge transfers from the metal adatoms to FeF3 (012) nanosheet. In other words, strong Na-F and K-F ionic bonds are formed after adsorption. Then, Bader charge analysis44,45 was further implemented to quantitatively describe charge transfer between Na/K atoms and FeF3 (012) nanosheet. As the Na/K atoms are absorbed at the hollow site (H-site), Na and K atoms lose the same valence electrons (+0.92 |e|). For the case of Na adsorption, charges of neighboring fluorides range from -0.57 |e| to -0.75 |e|,which makes Na-F bond show obvious character of ionic bond. Meanwhile, bond lengths of Na-F vary from 2.20 Å to 2.94 Å and coordination number of Na is six. Especially, the bond lengths of four Na-F bonds range from 2.20 Å to 2.55 Å and they are closed to bond length of ideal Na-F ionic bond (2.35 Å). That is to say, four stronger Na-F ionic bonds are formed. Besides, two weaker Na-F 7 / 36



bonds are formed with distances from 2.71 Å to 2.94 Å. Consequently, Na adatom is firmly adsorbed on the FeF3 (012) nanosheet and Na adatom perhaps to be located in static equilibrum. Thus, although strong interaction between Na and F ions exists, Na ions still can diffuse freely on the FeF3 (012) nanosheet.

Figure 1. Side (a) and top (b) views for isolated M (Na, K) adsorption sites (H, H1, B, B1and T) on the FeF3 (012) nanosheet; Top view of charge density difference and Bader charge for the most stable atomic configurations for (c) isolated Na and (d) isolated K on the FeF3 (012) nanosheet, the isosurface level is 0.001 e/Å3; charge density difference and Bader charge of (e) Na dimer and (f) K tetramer on FeF3 (012) nanosheet, the isosurface level is 0.0038 e/Å3. 8 / 36


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Then as well, for the case of K adsorption, charges of neighboring fluorides vary from -0.57 |e| to -0.73 |e|, six K-F ionic bonds are formed. Moreover, four strong K-F bonds are formed with distances from 2.49 to 2.81 Å since ideal K-F bond length is 2.71 Å. Besides, two weaker K-F bonds occur with distances of 3.01 Å. In the same way, K adatom is also perhaps to be located in static equilibrum when it is absorbed on the FeF3 (012) nanosheet, which contributes to diffusion of K atom. Next, we considered the cases of two Na and K atoms adsorption. By analysis of the relationship between relative energies of Na(K)/FeF3(012) nanosheet and interatomic distance of Na/K atoms , it is included that Na and K atoms both incline to get together in the form of Na dimer with a Na-Na distance of 3.20 Å and K dimer with a K-K separation of 3.57 Å, respectively. (details see Figures S-1~S-4 in Supporting Information). Now let us move to clarify the formation mechanism of multiple Na dimers and K dimers with increasing Na/K concentration (details see Figures S-5~S-8 in Supporting Information). After Na/K atoms are adsorbed on the FeF3 (012) nanosheet, they move to find the optimum adsorption sites, accompanying with structural relaxation. From the view of lattice matching, highly matching of K tetramer/FeF3 (012) nanosheet adsorption system can be obtained (details see Figure S-10(a) in Supporting Information). While Na tetramer possesses poorer matching degree with FeF3 (012) nanosheet relative to K tetramer (-4.42% vs. -1.73%) (details see Figure S-9 and Figure S-10(a) in Supporting Information). Therefore, Na atoms still remain the form of Na dimer and K atoms shift to form K tetramer. Moreover, 9 / 36



two K tetramers are difficult to get together due to the electrostatic repelling forces between them(details see Figure S-11 in Supporting Information). Then, we further calculated their charge density difference. Meanwhile, Bader analysis was carried out. The Na-induced and K-induced charge redistributions and corresponding local structures neighboring Na dimer and K tetramer were presented in Figure 1e and Figure 1f, respectively. As shown in Figure 1e and Figure 1f, it is noted that the electron states of Na dimer and K tetramer both are polarized. The Na dimer and K tetramer both induce electron redistribution. It is clear that Na and K atoms almost lose same valence electrons (+0.91 |e| vs. +0.90 |e|). Neighboring F atoms all obtain valence electrons from Na or K atoms. For each Na and K atoms, most of all, the strongest interaction between Na/K atoms and F atoms located at top layer take place because their most valence electrons are obtained by top-layer F atoms. For the case of Na dimer adsorption, charges of neighboring fluorides vary from -0.57 |e| to -0.80 |e|. Therefore, obvious Na-F ionic bond occurs. As a result, eight strong Na−F bonds are formed. Here, Na-F distances are in the range of 2.27Å-2.43Å, which are close to ideal ionic bond (2.35 Å). Besides, three more weaker Na−F bonds are formed with Na-F distances in the range of 2.73Å-2.88Å. Consequently, two Na atoms are brought together, forming Na dimer with a Na-Na separation of 3.20 Å. Similarly, in the case of K adsorption, the charges of fluorides near to K atoms vary from -0.58 |e| to -0.82 |e|, eighteen K-F bonds are formed. And K-F distances are in the range of 2.59 Å and 2.85 Å, which are all close to ideal ionic bond length (2.71 Å). Therefore, four K atoms are still connected together to form K tetramers, although 10 / 36


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repelling action exists among four K atoms. Besides, we further investigate the effect of Na dimer and K tetramer adsorption on the electronic structure of FeF3 (012) nanosheet. And the density of states (DOS) of FeF3 (012) nanosheet with and without Na/K adatoms were calculated. As shown in Figure 2, compared to FeF3 (012) nanosheet, Near the Fermi level, with s-states of Na/K introduced, stronger hybridization between Fe-3d and F-2p states can be observed, which indicates that the Fe-F ionic bond is further weakened. On the other hand, the adatoms donate electrons to the conduction band, thus causing the conduction band to move downward. Therefore,the band gap of the system containing Na dimer or K tetramer decreases obviously. And it is favor to improve the conductivity of FeF3 (012) nanosheet after Na/K atoms adsorption. In this regard, FeF3 (012) nanosheet can be acted as a potential material for NIBs and KIBs.

Figure 2. Density of states of (a) FeF3 (012) nanosheet, (b) Na dimer/FeF3 (012) 11 / 36



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nanosheet and (c) K tetramer/FeF3 (012) nanosheet. Now let us move to further investigate the effect of Na/K concentration on the stability of Na/K adsorbed FeF3 (012) nanosheet. In our work, Adsorption energy ( EAds ( x) ) can be defined as EAds ( x ) 

Where E (M x FeF3 )

1 ( E (M xFeF3 )  E (FeF3 )  x μM ) x

and E (FeF3 )

(4)

denote the total energies of M/FeF3(012)

nanosheet (M = Na, K) and FeF3 (012) nanosheet, respectively. μM and x indicate the chemical potential of M and Na/K concentration, respectively. After geometrical relaxation, the stable atomic structures of Na/K adsorption on the FeF3 (012) nanosheet with different Na/K concentrations can be obtained (details see Figures S-12~S-13 in Supporting Information). Figure 3 shows the relationship between the Na/K concentration (x) and adsorption energy of NaxFeF3 and KxFeF3. It is noted that adsorption energy increases with increasing Na/K concentration and the adsorption energy is still negative at even high Na/K content. In other words, although it will become more and more difficult for Na/K adsorption accompanying the increase of Na/K concentration, it is feasible to adsorption with high Na/K content on the FeF3 (012) nanosheet. Besides, compared with adsorption energies of Na and K adatoms , it is clear that K adatoms prefer to be adsorbed on the FeF3 (012) nanosheet. That is to say, FeF3 (012) nanosheet can accommodate more K adatoms than Na adatoms, which contributes to higher capacity.

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Figure 3. Adsorption energy of NaxFeF3 and KxFeF3 with increasing Na/K concentration (x). 3.2 Diffusion of Na/K Adatom on FeF3 (012) Nanosheet It is well known that the kinetics of ion diffusion largely determine the rate performance of electrode materials.46 Thus, we turned our attention to explore Na/K-ion diffusion kinetics. We first investigated the diffusion behaviors of single Na/K ion on the FeF3 (012) nanosheet. In the light of the symmetric structure of FeF3 (012) nanosheet, three possible Na/K diffusion paths (path1, path2 and path3) between neighboring hollow sites (H-sites) were considered. As shown in Figure 4a,b, path1 is via bridge site (B) ( H→B→H ), path2 is via another bridge site (B1)

(H→B1→H ) and path3 is along H-T-H sites ( H→T→H ). Here, T represents top site.

And the energy barriers associated with those pathways were illustrated on the right side of Figure 4a,b. Compared with K-ion diffusion, it is noted that path3 changes largely for Na-ion diffusion. As a matter of fact, the path3 becomes the combination 13 / 36



of path2 and path1 due to smaller radius and formula weight of Na atom than those of K atom. And the energy barriers along path1, path2 and path3 are 0.18 eV, 0.26 eV and 0.26 eV, respectively, which indicate that path1 is the fastest diffusion process. Moreover, the lowest value (0.18 eV) approaches the energy barriers of Na ion on other 2D materials, such as SiSe monolayer (0.16 eV).47 ReS2 (0.16 eV)48 and BP (0.22 eV).49 In order to further explore the reason for difference of energy barriers along different diffusion pathways, the local structures of transition states (B-site, B1-site) in path1 and path2 were shown in Figure 4c. Minimum Na-F distances for transition states are 2.18 Å and 2.08 Å, respectively. This means that Na atom demands more energy to disrupt F-Na (B1-site) bond, which triggers larger energy barrier during Na atom strides over B1-site. For the diffusion of isolated K, among path1, path2 and path3, path3 still keep along H-T-H sites. Similarly, path1 is the easiest pathway to spread owing to its lowest energy barrier (0.26 eV). It is confirmed that FeF3 (012) nanosheet is prior to MoN2 nanosheet due to its lower K-ion diffusion energy barrier (0.26 eV vs. 0.49 eV).50 Therefore, FeF3 (012) nanosheet belongs to a promising 2D cathode material for KIBs. Similarly, Figure 4d shows the local structures of transition states (B, B1 and T) in three pathways to study the tendency of these energy barriers. It is noted that B-site possesses the longest distance of K-F (2.51 Å). Thus, K ion perhaps require a minimum energy to break the K-F bond and complete diffusion along path1.

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Figure 4. Isolated (a) Na and (b) K diffusions on FeF3 (012). Top views of Na/K diffusion pathways: path1: H→B→H ; path2: H→B1→H ; path3: H→T→H ; Local structures of transition states for (c) isolated Na and (d) K on the FeF3 (012) nanosheet.

15 / 36



Figure 5. (a) Top view of the Na dimer diffusion pathway and (b) the corresponding curve of energy barrier along path1 for Na dimer on the FeF3 (012) nanosheet.

Next, we turned our attention to investigate diffusion behaviors of Na dimer and K tetramer. For Na dimer, two diffusion pathways were carefully detected and they were labeled as path1 and path2 (details see Figure S-14 in Supporting Information), respectively. And the optimal diffusion pathway was obtained, namely path1: ① →

② → ③ → ④ → ⑤ → ⑥ → ⑦ → ⑧ . For path1, as indicated in Figure 5a, as a 16 / 36


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whole, Na dimer prefers to migrate from one H-site to a neighboring H-site via B-site as the transition state. And the corresponding energy barrier curve was shown in Figure 5b. It is found that the energy barrier along path1 is 0.45 eV. Compared with isolated Na diffusion, energy barrier of Na dimer is closed to two times that of isolated Na. Thus, outstanding multiple Na diffusion kinetics appear on the FeF3 (012) nanosheet. To further interpret the diffusion mechanism of Na dimer on the FeF3 (012) nanosheet, the local structure of intermediate state along path1 was presented in Figure 6a. Na1 atom lies at the H-site. Meanwhile, Na2 is located at B-site and Na-F distances are 2.14 Å and 2.16 Å. Compared with ideal Na-F ionic bond length (2.35 Å), two strong Na-F bonds form, which may make the sodium atoms be located in static equilibrum. Therefore, Na dimer can still migrate very fast although strong Na-F bonds exist.

Figure 6. Locate structures of saddle points for (a) Na dimer and (b) K tetramer (Top view), respectively. 17 / 36



Next, we further investigated diffusion of K tetramer on the FeF3 (012) nanosheet. Combined with diffusion law of isolated K, we considered diffusion path of K tetramer along the zigzag direction was shown in Figure 7a. And it was labeled as: ① → ② → ③ → ④ → ⑤ → ⑥ → ⑦ → ⑧ → ⑨ . Each K atom passes

through B-site to adjacent H-site, possessing the lowest diffusion barrier. The corresponding energy barrier of K tetramer is 0.43 eV(see Figure 7b). Interestingly, energy barrier of K tetramer is obviously lower than four times that of isolate K (0.43 eV vs. 1.04 eV). Therefore, even for multi K diffusion, K diffusion on the FeF3 (012) nanosheet may show excellent kinetics performance. To further clarify diffusion process, the structure of saddle point along path1 was shown in Figure 6b. K1 is located on the most stable adsorption site (H-site). Reference Figure S-7, K3 and K4 form a stable dimer structure and the distance between them is 3.63 Å. What's more, K2 lies in B-site and the distances between K2 and neighboring F atoms are 2.44 Å and 2.54 Å. Two strong K-F bonds are formed since the ideal K-F ionic bond length is 2.71 Å. To a certain extent, K tetramer can maintain good diffusion performance because K atoms are located in static equilibrum.

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Figure 7. (a) Schematic representations of path1 for K tetramer diffusion on the FeF3 (012) nanosheet (top view). (b) the curve of diffusion energy barrier along the optimized pathway for K tetramer. 19 / 36



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To further assess diffusivity of Na dimer and K tetramer on FeF3 (012) nanosheet at 25℃, their corresponding diffusion coefficients are calculated and presented in Table 1. As shown in Table 1, diffusion coefficients of Na dimer and K tetramer are 3.32×10-10 cm2·s-1 and 4.22×10-10 cm2·s-1, respectively. This indicates that the rate performance of FeF3 (012) nanosheet is better than that of other focused materials for NIBs or KIBs51-53. For example, diffusion coefficient of Na on FeF3 (012)

nanosheet

is 105 times than Na4Mn9O18.51 Besides, compared with Na-ion batteries, better rate performance can be obtained when FeF3 (012) nanosheet is acted as cathode material in K-ion batteries. Thus, FeF3 (012) nanosheet is a nice choice for both NIBs and KIBs. Table 1. Hopping Distances, Energy Barriers and Diffusion Coefficients at 25℃ for Na Dimer and K Tetramer Migration on the FeF3 (012) Nanosheet. path

Hopping distances

Energy barriers

Diffusion coefficients

(Å)

(eV)

(cm2·s-1)

3.43

0.45

3.32×10-10

2.63

0.43

4.22×10-10

Na dimer path1 K tetramer path1

3.3 Theoretical Voltage and Capacity In the view of practical application, theoretical voltage and capacity can be 20 / 36


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implemented to evaluate the electrochemical properties of NIBs and KIBs to some extent. Therefore, we further evaluated the electrochemical properties of FeF3 (012) nanosheet by calculating theoretical voltage and capacity. Then, the electrochemical reaction between FeF3 (012) and M (M is Na/K) can be written as: M x1 FeF3  ( x2  x1 )M   M x2 FeF3

(5)

And the theoretical voltage (Vave ) is calculated according to following expression:54,55

Vave  

E( x2 )  E( x1 )  ( x2  x1 )EM x2  x1

(6)

Where, x1 and x2 represent the number of Na/K atoms. E(x2) and E(x1) indicate the total energies of the FeF3 (012) with x2 (x1) Na/K atoms. EM denotes the total energy of isolated Na/K atom. During adsorption reaction between FeF3 (012) nanosheet and Na/K, the expected theoretical capacity (C) can be expressed as:

C=

nN0 e 0

×

1 1×10-3 ×3600

(7)

where n denotes the number of Na/K involving electrochemical process. N0 represents Avogadro’s constant, e and M0 are electron charge and formula weight of FeF3 (012) nanosheet after absorbing Na/K atoms. The relationship between theoretical voltage of FeF3 (012) nanosheet and its theoretical capacity was presented in Figure 8. As shown in Figure 8, when FeF3 (012) nanosheet is applied in NIBs, the calculated theoretical voltage of decreases from 3.74 V to 3.29 V with specific capacity varying from 139.4 mAh/g to 197.3 mAh/g. Compared with NaFeF3 nanoplates

27

and sheet-like FeF3,33 FeF3 (012) nanosheet exhibits most stable voltage

plateau. Similarly, when FeF3 (012) nanosheet is utilized in KIBs, it is noted that FeF3 21 / 36



(012) nanosheet also possesses stable and high voltage plateau.

Figure 8. The theoretical voltage curves of FeF3 (012) nanosheet as a function of specific capacity in the Na-ion and K-ion cells. The experimental discharge curves of NaFeF3 nanoplates (10-600 nm)27 and sheet-like FeF333 in the Na-ion cell for comparison. 3.5 Mechanical Properties of Multiple K Adsorbed FeF3 (012) Nanosheet As the structure of FeF3 (012) nanosheet undergoes considerable structural changes during potassiation process, morphological change and electrode fracture are likely to occur. Accordingly, a problem of capacity loss arises during charge-discharge cycles.56-59 Besides, in-plane stiffness is a fundamental physical quantity and it can be implemented to elevate the mechanical properties of materials.60,61 Next, we further 22 / 36


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discussed the in-plane stiffness of FeF3 (012) nanosheet as a function of potassium concentration (x) to understand the features influencing the mechanical behavior of potassium on the FeF3 (012) nanosheet. The in-plane stiffness ( C2D ) of KxFeF3 (see Figure 9a), εx and εy represent stress applied along armchair and zigzag directions can be obtained via the relation as follows:62,63

C2D =

∂2 E ∂δ2

/S0

(8)

Where E is the total energy of the strain system, δ is the applied uniaxial strain, and S0 is the area of optimized cell. The variation of in-plane stiffness for FeF3 nanosheet is presented with increasing K concentration (x), as shown in Figure 9b. It is obvious that in-plane stiffness of FeF3 (012) nanosheet is equal to 60 N/m along armchair (Cx), while its value is 69 N/m along zigzag direction (Cy), which is close to the values of typical 2D materials with excellent plasticity in recharged batteries (20-100 N/m).64-67 Most importantly, Cx decreases from 60 N/m to 47 N/m and Cy varies from 69 N/m to 55 N/m. In other words, although the in-plane stiffness decays gradually, it still holds 47 N/m at nearly 100% of K concentration (x), which indicates that FeF3 (012) nanosheet is appropriate to be fabricated as flexible electrode materials in K-ion batteries. Interestingly, the discrepancy between Cx and Cy is small (Cy/Cx is close to 1). Moreover, the value of Cy/Cx keeps stable with increasing K concentration (x). That is to say, FeF3 (012) nanosheet still can possess good isotropic property, even if a large number of potassium insert into FeF3 (012) nanosheet. Due to close relationship between isotropic property and structural stability of materials,68 it is confirmed that FeF3 (012) 23 / 36



nanosheet can maintain excellent stability during potassium insertion and extraction.

Figure 9. In-plane stiffness of FeF3 (012) nanosheet in zigzag (Cx) and armchair direction (Cy) with increasing K concentration. (a) the crystal model of FeF3 (012) nanosheet applied by stress in two different directions. εx and εy represent stress applied along armchair and zigzag directions. (b) εx, εy and Cy/Cx as a function of potassium concentration (x).

4. CONCLUSIONS We have theoretically investigated the Na/K storage mechanism on the FeF3 (012) . By calculating adsorption energy at different adsorption site, Na and K adatoms both prefer to occupy the hollow site (H-site). For multiple Na/K atoms adsorption, Na atoms tend to aggregate in the form of Na dimer, while K atoms prefer to get together in the form of K tetramer. For Na dimer and K tetramer, adatoms are still located at H-sites. In addition, FeF3 (012) nanosheet can adsorb Na/K atoms freely and it shows excellent mechanical properties even in high Na/K concentration, suggesting that its strong damage resistance during sodiation or potassiation. In addition, for isolated 24 / 36


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Na/K atom diffusion, the energy barriers of Na and K are 0.18 eV and 0.26 eV along their optimum pathways, respectively. And similar anisotropic energy barriers occur on Na dimer and K tetramer. Interestingly, energy barriers of K tetramer is lower than that of Na dimer( 0.43 eV vs. 0.45 eV). As a result, K tetramer possesses larger diffusion coefficient than Na dimer (4.22×10-10 cm2·s-1 vs.3.32×10-10 cm2·s-1), which indicates that K tetramer can diffuse faster than Na dimer on the FeF3 (012) nanosheet. Relative to the case of Na adsorption, FeF3 (012) nanosheet would obtain better rate performance in the case of K adsorption. In addition, when FeF3 (012) nanosheet and potassium are used as cathode and anode materials, it is noted that FeF3 (012) nanosheet exhibits more excellent electrochemical properties (higher initial discharge voltage and more stable voltage plateau) than NIBs. Besides, FeF3 (012) nanosheet is appropriate to be fabricated as flexible cathode materials in KIBs. ASSOCIATED CONTENT Supporting information Details of calculations including the relative energies of the adsorption configurations with two Na or two K atoms on the FeF3 (012) nanosheet, the relative energies of Na/FeF3(012) nanosheet with increasing distance between Na dimers, the relative energies of K/FeF3(012) nanosheet with increasing distance between K dimers,Matching degrees between Na tetramer (or K tetramer) and FeF3(012) nanosheet, the relative energies of K/FeF3(012) nanosheet with increasing distance between K tetramers,the optimized structures of FeF3 (012) nanosheet with different Na/K concentrations and the diffusion path (path2) of Na dimer on the FeF3 (012) 25 / 36



nanosheet.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] (Zhenhua Yang) *E-mail: [email protected] (Xingqiang Shi) ORCID Zhenhua Yang: 0000-0002-3967-6249 Xingqiang Shi: 0000-0003-2029-1506 Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS This research is supported by the National Natural Science Foundation of China (Grant No. 21573187), Hunan Provincial Natural Science Foundation of China (Grant No. 2017JJ2246), Opening Foundation of Key Laboratory of Materials Design and Preparation Technology of Hunan Province (Grant No. KF20140701), Shenzhen Fundamental Research Foundation (Grant No. JCYJ20170817105007999) and the Center for Computational Science and Engineering of Southern University of Science and Technology. REFERENCES (1) Shadike, Z.; Zhou, Y. N.; Chen, L. L.; Wu, Q.; Yue, J. L.; Zhang, N.; Yang, X. Q.; Gu, L.; Liu, X. S.; Shi, S. Q.; Fu, Z. W. Antisite Occupation Induced Single Anionic 26 / 36


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K on FeF 3

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