Theoretical Prediction of Anode Materials in Li-Ion Batteries on

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Theoretical Prediction of Anode Materials in LiIon Batteries on Layered Black and Blue Phosphorus Qingfang Li, Chun-Gang Duan, Xiangang Wan, and Jer-Lai Kuo J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp512411g • Publication Date (Web): 01 Apr 2015 Downloaded from http://pubs.acs.org on April 9, 2015

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The Journal of Physical Chemistry

Theoretical Prediction of Anode Materials in Li-Ion Batteries on Layered Black and Blue Phosphorus Qing-Fang Li1,2 , Chun-Gang Duan4 , X. G. Wan2,3∗ , and Jer-Lai Kuo5 1

Department of Physics, Nanjing University of Information Science & Technology, Nanjing 210044, China. 2

National Laboratory of Solid State Microstructures,

College of Physics, Nanjing University, Nanjing, 210093, China. 3

Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China. 4

Key Laboratory of Polar Materials and Devices, Ministry of Education, East China Normal University, Shanghai 200062, China

5

Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan.

Black phosphorus (P) has been considered as a promising candidate for anodes due to its ability to absorb large amount of Li atoms. Unfortunately, lithiation of bulk black P induces huge structural deformation, which limits its application. Here, based on the density functional theory calculation, we predict that the newly found two-dimensional (2D) black and blue P are good electrodes for high-capacity lithium-ion batteries. Our theoretical calculations indicate that in contrast to bulk black P, the mono-layer and double-layer black and blue P can maintain their layered structures. during lithiation and delithiation cycles. Moreover, it is found that Li diffusion on the the surfaces of black and blue P has relatively low energy barriers (< 0.4eV), and the single-layer blue P and double-layer black and blue P possess high charge capacities.

∗

E-mail address:[email protected]

ACS Paragon Plus Environment


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I.

INTRODUCTION

Rechargeable lithium batteries (RLBs) with high energy density are urgently demanded for portable power and grid applications [1, 2]. The energy density of RLBs depends critically on the specific charge capacity of the constituent electrodes [3, 4]. Currently the most commonly used anode material is graphite due to its effective performance [5–7]. Unfortunately, graphite anode has only a moderate theoretical capacity (372 mAh·g−1 ) and also suffer from poor rate capability [5, 8]. Other potential anode materials, such as silicon and transition-metal oxides, also face some critical issues, including drastic volume changes during Li intercalation/deintercalation, high working potentials, large irreversible capacities and low Li diffusivities [9, 10]. Therefore, it is necessary to search new anode materials with high-rate capabilities and good cycling performances. Bulk black phosphorus (P) had been demonstrated as a good anode material of RLBs [11, 12]. By using high-energy mechanical milling method, Park and Sohn found that bulk black P possessed a high charge capacity of 1279 mAh·g−1 , unfortunately the capacity decreased to about 220 mAh·g−1 after 30 charge/discharge cycles [11]. Moreover, it had been found that various Lix P phases, such as LiP7 , LiP5 , Li3 P7 and LiP, will form in the process of lithium intercalation into bulk black P, and the layered structure trends to crack during lithiation [11–13]. The lithiation-induced tensile stress and layered structure cracking in bulk black P limit its commercialization. The structural changes and stresses may be mitigated by manipulating the structural patterns of anode materials such as nanowires, hollow nanoparticles and two-dimensional (2D) thin films [14]. Due to their high surface-volume ratio and unique electronic properties distinguished from their bulk counterparts, the layered 2D materials have been considered as potential anode materials with high-performance RLBs [15–19]. Very recently, a new 2D compound, monolayer black P had been found and attracted a great deal of attention [20–29]. Monolayer black P is, besides graphene, the only stable elemental 2D materials that can be mechanically exfoliated. Soon after the discovery of 2D black P, Zhu et al. [29] theoretically proposed another phase of phosphorus called ”blue phosphorus (blue P)”. Their numerical calculations reveal the blue P is nearly as stable as black P [29]. Although, so far, the blue P is still not fabricated by experiment, however, blue P had attracted a great deal of interest [29–33]. Both few-layer black and blue P have large surface-volume ratio, moreover, they form a puckered surface, which provide more space for lithium storage. Therefore, few-layer black and blue P may serve as high-capacity hosts of Li in RIBs. In this paper, using density functional theory calculation, we explore the suitability of 2D black and blue P as the host materials for Li. We focus on single-layer (SL) and double-layer (DL) black and blue P, and provide atomic-level


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insights into the Li diffusion in these systems. We identified the favorable adsorption sites of lithium and calculated the Li diffusion barriers. Our numerical results indicate that the BL black P, ML and BL blue P may be good candidates for the anode materials of Li-ion batteries.

II.

CALCULATION METHODS

Our calculations are carried out by employing the method of projector augmented wave potentials [34] based on density functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP) code [35, 36]. We use generalized gradient approximation (GGA) with the parametrization of Perdew-Burke-Ernzerhof(PBE) [37]. It had been found that the Van der Waals interaction is quite important for black P [38]. Thus we include it by using the empirical correction scheme of Grimme (DFT+D2) [39], as implemented in the VASP code [40]. The energy cutoff for expansion of wave functions and potentials is 450 eV. The entire systems are relaxed by conjugated gradient method till the force on each atom is less than 1 meV/˚ A. A vacuum of 20˚ A is created along the Z axis on both sides of the layer (perpendicular to the layered black and blue P) to safely avoid the interaction between the periodically repeated structures. The diffusion barriers are obtained using the standard nudged elastic band method (NEB) [41].

III.

RESULTS AND DISCUSSION

We optimize both the in-plane cells and all atomic positions, and the numerical lattice constants are 3.32 ˚ A and 4.57 ˚ A for SL black P, and 3.34 ˚ A and 3.34 ˚ A for SL blue P, respectively, which agree well with previous results [21, 23, 29]. We also optimized the structures of DL black and blue P. There are three possible stacking orders for DL P [23]. Our calculations demonstrate that the AB-stacking is the most favorable configuration for DL black P, while DL blue P is AA-stacking. The calculated in-plane lattice constant of DL black P is 3.33 ˚ A and 4.52 ˚ A, and the interlayer distance is 3.20 ˚ A, which is comparable with previous results [21, 23]. The optimized in-place lattice constant of DL blue P is 3.34˚ A and 3.34˚ A with interlay distance of 3.20 ˚ A. Based on the primitive cell, different models including 2 × 2, 3 × 3 and 4 × 4 supercells have been used to analyze the Li adsorption. We find that the adsorption energies per Li atom on black P almost do not change with the increase of supercell size, and the adsorption energies per Li atom on 3 × 3 and 4 × 4 supercells for blue P almost remain the same. Consequently we only present the results of 2 × 2 black P supercell and 3 × 3 blue P supercell (Fig.1) in the following discussion. To check the lithium adsorption ability, we investigated the adsorption behavior of Li on the black and blue P. We



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optimize the various geometries of Li on the black and blue P. The most stable configurations are shown in Figure 2 and 3. The adsorption energy of lithium is defined as Ead =(ELi+P -nELi - EP )/n. Here, ELi+P and EP are the total energies of P with and without Li adatoms, respectively, ELi is the energy of a free Li atom, and n is the number of adsorbed Li atoms. We use the notation of Lix P1−x to distinguish the lithium content. For example, the pristine black or blue P corresponds to x = 0. We first discuss the case of Li adsorption on SL black P (Figure 2(a)-(d)). For one Li adatom in the 2 × 2 supercell (namely, SL Black P-Li0.06 P0.94 ), the Li atom prefers to occupy the hollow (H) site, where Li has three nearest neighbor P atoms as shown in Figure 2(a).The nearest-neighbor Li-P bond lengths are 2.49, 2.55 and 2.55˚ A, respectively. The corresponding adsorption energy is -1.96 eV. The H sites remain the most favorable adsorption sites for two-atom and four-atom adsorption (i.e. SL black P-Li0.11 P0.89 and P-Li0.20 P0.80 ). The calculated adsorption energies are Ead =-1.96 eV and -1.97 eV, respectively. In these cases, half of the Li adatoms are situated above and half below the black P monolayer. Our calculations show that further increasing the Li adsorption will change the structure significantly as shown in Figure 2(d). The adsorption energy of eight-atom adsorption (i.e. is SL black P-Li0.33 P0.67 ) is -2.51eV, while the system cannot return back to 2D like structure by removal of the Li atoms because the P atoms are pushed out of the plane by the attached lithium. The binding energy of the highly puckered P after complete delithiation is 0.34eV/atom higher than that of the pristine black P. We thus believe that the adsorption of four Li atoms is the upper limit. For one Li atom adsorption on SL blue P (namely, SL blue P-Li0.05 P0.95 ), adsorption directly above a P atom (i.e., top site as shown in Figure 2(e)) is the most stable adsorption site with Ead =-2.02 eV. The three nearest-neighbor Li-P bonds are equivalent with a bond length of 2.55 ˚ A. While, adsorption above the center of the hexagonal phosphorus ring (hollow site) and at the bridge (B) site between two neighbor P atoms is slightly weaker with Ead =-1.94 eV and Ead =-1.90 eV, respectively. The top sites remain the most favored sites with increasing the lithium adsorption as shown in Figure 2(f). Similar with the case of SL black P, for the SL blue P, the adatoms are also distributed above and below the layer equally. When the lithium content becomes x = 0.25, the Li atoms will only locate at one side of the layer and form stripes as shown in Figure 2(g). The absorption energy is still negative even the Li coverage reach a quite large value of x = 0.5, and for this case half of the adatoms reside above and half of them below the monolayer blue P as shown in Figure 2(h)). The corresponding adsorption energy is 1.70eV. Adsorption at hollow site is slightly weaker with Ead =-1.69 eV. When the adsorption x > 0.5, the layer structure becomes unstable, thus x = 0.5 is the maximum Li adsorption for SL blue P.


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We now turn to the atomic structures of lithiated DL black P( Figure 3 (a)-(e)). For one Li adatom in the DL black P (namely, DL black P-Li0.03 P0.97 ), Li adsorbs preferably at the H site between two atomic layers with Ead =-2.38 eV. The lithium absorbed at the H site of the external atomic layer is less favorable with Ead =-1.99 eV. The H sites between two atomic layers remains the most favourable sites for two-atom, four-atom and eight-atom adsorption as shown in Figure 3 (b)-(d). The adatoms gradually occupy the two external surfaces of the DL black P with increasing Li concentration. When the Li coverage becomes x = 0.33 (Figure 3 (e)), half of the Li adatoms reside above and half of them below the external surfaces. When the Li coverage is further increased, the layer structure becomes unstable. Therefore we use x =0.33 to represent the highest adsorption concentration of DL black P. It is noteworthy that the two atomic layers move relatively to each other when the Li atoms adsorb. For example, for x=0.06, the stacking structure changes from the AB-stacking to AC-stacking during lithiation. However, the systems still remain the layer structures. We also gather the atomic structures of lithiated DL blue P in Figure 3 (f)-(j). As is the case in the SL structure, one Li atom preferably occupies the top site, but in the case of DL blue P (namely, DL blue P-Li0.03 P0.97 ) Li prefers to occupy the hollow site between two atomic layers and it has six nearest neighbor P atoms. The calculated adsorption energy is Ead =-2.62 eV. While, adsorption at hollow site of the external surfaces or at the top site between two atomic layers is less favorable with Ead =-2.06 eV and Ead =-2.42 eV, respectively. The hollow sites remain the most favorable sites for two-atom and eight-atom adsorption (i.e. DL blue P-Li0.05 P0.95 and P-Li0.20 P0.80 ). When the Li coverage becomes x = 0.33, Li atoms occupy the hollow sites of the interior and the top sites of one side of the two external surfaces as shown in Figure 3 (i). For twenty-seven lithium atoms (x = 0.43), a third of Li atoms reside at the hollow sites of the interior and the other Li atoms reside at the top site of the two external surfaces with Ead =-1.97 eV. When the Li coverage is x > 0.43, the layered structure is unstable. Therefore, we believe that adsorption twenty-seven Li atoms (i.e. DL blue P-Li0.43 P0.57 ) is the up limit. We find that the lithiated behavior of DL black and blue P is different. For DL black P, Li atoms prefer to fill the interior gallery (x ≤0.25) , then the Li adatoms shift from the interior gallery to the outermost galleries fully when the Li concentration increases. For DL blue P, Li atoms fill the interior gallery first, then fully fill one external gallery, and finally the other external gallery. In general, the more the absorbed Li atoms are, the greater the influence of absorbed atoms on crystal structure is. Thus we only discuss the effects of the Li atoms on crystal structure with the highest lithium content in the following: the distortion of black P is negligible in SL-Li0.20 P0.8 where the distance between two atomic layers increases by 0.04 ˚ A, and the puckered height (i. e. thickness of single layer) in the pristine SL black P is 2.11 ˚ A. However, the surface



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distortion of DL black P-Li0.33 P0.67 is pronounced. The structure loses the initially AB arrangement, and the distance between top/bottom two P planes increases to 2.23/2.25 ˚ A (2.12 ˚ A in pure DL black P). It is found a slight structural change in SL blue P-Li0.5 P0.5 where the distance between two adjacent planes increases by 4%, and the distance between top (bottom) two atomic layers only increases by 2% in DL blue P-Li0.43 P0.57 . We further optimize the unit cell of lithiated black and blue P and we find the overall change in the lattice constants is negligible. Therefore, the black and blue P layers show very small structural changes upon lithiation. More importantly, optimizing both the in-plane cells and all atomic positions after complete delithiation, it is found that the 2D black and blue P surfaces are restored to the form of the pristine structures in contrast to bulk black P which undergoes severe structural changes due to plastic deformation [11, 12]. We summarize how the adsorption energies vary with adatom concentration (Figure 4). The adsorption energy remain almost the same for the lithiated SL black P. Going from the pristine to the lithiated SL (DL) blue P with the highest Li concentration, there is a little change in the adsorption energy which spans only ∼ 0.3 (0.6) eV. However, the adsorption energy of DL black P changes about 1.0 eV during lithiated process. Therefore, the working potential of an electrode based on black and blue P should be relatively flat except DL black P, which also happens to be one attractive feature in graphite, the most commercially successful anode for lithium-ion batteries. The energies should compare with the bulk energy of Li[42]. This is a better definition in the context of RIBs, as the formation of bulk Li represents anode failure and dendrite formation. As can be seen in Figure 4, the calculated adsorption energies for all systems are lower than the energy of bulk Li (-1.62 eV atom−1 ), which prevents the clustering of Li atoms during lithiated process. In order to explain the trend of adsorption energies, the charge transfers from adatom to black/blue P are calculated by bader charge analysis [43]. Each lithium adatom donates about 0.74e∼0.88e and 0.78e∼0.88e to P in black and blue P, respectively, which results in partially cationic Li atom. Furthermore, we discuss the interactions between Li and phosphorus. The electron localization function (ELF) index has been found very useful in describing and visualizing the atomic shells and chemical bonds in solids [44]. The essence of interactions between Li and P for all configurations is similar, thus, we only present the ELF of one Li adatom on SL black and blue P in Figure 5. ELF takes values in the range between 0 and 1, where ELF=1 corresponds to perfect localization and ELF=1/2 if for uniform electron gas[45, 46]. It can be seen that the values of ELF at the Li and P sites is large which indicates strong local character. The ELF between Li and P is negligibly small. Therefore the chemical bond of Li on black/blue P is mainly dominated by ionic components. On the other hand, the repulsion among Li ions enhances with the increase of Li concentration. The cooperative effect of the static charge transfer and the repulsive interaction results in the


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subtle change of adsorption energy of SL black P, SL and DL blue P. Obviously, the mechanism of change in the adsorption energy of DL black P is different. At low Li content where Li resides in interior gallery, the adsorption energy decreases as the Li concentration increases which mainly attributes to the surface reconstruction of lithiated DL black P. The manifestation of electric effects in geometry is the expansion of the P-P distances between two atomic layers. At high Li coverage, the mechanism of the change in the adsorption energy is similar with that in SL black P. It is noted that the Li atoms bind stronger with DL black/blue P than SL black/blue P, therefore the lithated DL phosphorus is more stable than the SL ones. To discuss the capacity, we calculated charge capacities which are obtained with the formula, Cth =(F·nLi )/(3.6manode ), where F is Faraday constant (96500 C/mol), nLi is the number of lithium per formula unit of the electrode material (Lix P1−x ), and manode stands for the mass of P in Lix P1−x . The theoretical charge capacities of SL and DL black P are 216 and 433 mAh·g−1 , respectively. The charge capacities of SL and DL blue P are 865 and 649 mAh·g−1 . As noted above, the charge capacities of the DL black P, SL and DL blue P are significantly higher than that of graphite (372 mAh·g−1 ). To further understand the binding mechanism between Li and the black/blue P, we analyze the electronic properties of lithiated black/blue P. Figure 6 indicates the density of states of pristine black/blue P and lithiated black/blue P with the lowest and highest Li adsorption concentration. Comparing with the pristine black/blue P, it can be seen that the Li adatoms not only donate electron into black/blue P but also change the band structure of black/blue P and induce a semiconductor-metal transition, which again shows the considerable interaction between Li adatoms and black/blue P. It is well known that the rate performance of the electrode material is determined by the electrical conductivity and lithium diffusion characters. Thus the diffusion of lithium adatom on black and blue phosphorus is examined in our calculations. For surface diffusion of one lithium on the monolayer black P, we consider two different diffusion paths which are the zigzag and armchair directions, respectively (Figure 7(a)). In the case of one lithium adatom on the black P, Li occupies the hollow site with three nearest neighbor P atoms. As a Li atom at hollow site moves along the zigzag direction, it passes over the bridge site (b site) to the nearest neighbor hollow site (c site) by overcoming an energy barrier of 0.12 eV, then Li atom hops from c site to the next hollow site (e site). As Li diffuses along the armchair direction, it must pass over the top site. This diffusion pathway has a higher energy barrier (0.84 eV) as shown in Figure 7 (a). Thus, one lithium atom prefers to diffuse along zigzag direction. For monolayer blue P, the pathway is characterized by the two symmetrical maximums and one local minimum as shown in Figure 7(b). Positions above the P atoms (position a and b in Figure 7(b)) represent the absolute energy minima, and position



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at the hollow site represents the secondary adsorption minimum. Therefore, an optimal path of lithium diffusion is from a top site to the nearest neighboring top site passing through a hollow site. The calculated diffusion barrier is 0.16eV, which is slightly higher than that in SL black P. Compared with the lithium diffusion on perfect graphene (0.277 eV for diffusion barrier ) [47]and silicene (0.23 eV for diffusion barrier) [15], the lithium diffusion barriers on SL black/blue phosphorus decrease by about 0.16/0.12 and 0.11/0.07 eV, respectively. This suggests that the rate performance of black/blue P can be better than graphene and silicene. Another possible pathway is Li diffusion from one hollow site to a neighboring one through the black/blue phosphorus monolayer (Figure 8 (a,b)). The pathways involve energy barriers of 1.06 and 2.38 eV for black and blue P, respectively. Therefore, the lithium diffusion is faster in-plane directions. And Li diffusion through the black/blue P sheet is slow at ambient temperature without any external conditions, however, the barrier of Li diffusion through the black/blue P layer is significantly lower than that of Li diffusion in the direction perpendicular to the graphene sheet(9.80/8.38 eV) [48, 49]. Especially, for black P, the diffusion barrier is even lower than that of defective graphene [48, 49]. It is clear that the Li ion can easily diffuse from one side to the other side in SL black and blue P compared with the graphene. In the high-coverage limit, the diffusion of Li is modeled by removing a lithium atom from the highest coverage as shown in Figure 8(c, d). For black P, similar with the case of the low coverage, the Li prefers to diffuse along armchair direction, which involves an energy barrier of 0.13 eV. For SL blue P-Li0.49 P0.51 , an optimal diffusion is from a hollow site to a nearest neighboring one. In the case, the diffusion barrier is 0.24 eV as lithium passes over a top site. We also study the effect of the additional atomic layer in the DL black and blue P on the energies of diffusion. One adatom diffuses between two hollow sites of the DL black P surface by overcoming a 0.28 eV energy barrier(Figure 9(a)). For DL blue P, a Li atom hops between the nearest-neighbor hollow sites passing through a bridge site at which point lithium is bonded to two neighbor P atoms. The calculated diffusion barrier of this pathway is 0.39 eV (Figure 9(b)). The diffusion character and energy barriers on external surface are similar with the case of singlelayer phosphorus. The lithium diffusion energy barriers on both DL black and blue P is much smaller than that of DL silicene (0.75 eV) [15]. For DL black P-Li0.32 P0.68 (high Li content), there are two possible diffusion pathways as shown in Figure 9 (c). The diffusion barriers for Li are 0.21eV and 0.19eV along AB (zigzag direction) and AC directions, respectively. The diffusion barrier along armchair direction is more than 1.0eV, therefore we do not present the results. For DL blue P-Li0.42 P0.58 , Li hops from a hollow site to the nearest neighbor one passing over a top site (Figure 9 (d)). The corresponding energy barrier is 0.22 eV. Similar with the case in the SL P, it is more difficult that Li moves through both atomic layers than on surface. Taking the double-layer blue P for example, the energy barrier


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is 2.18 eV when a Li atom migrates through both atomic layers. We therefore do not further consider this case. In summary, we have elucidated the Li adsorption character on SL and DL black/blue P using the density functional theory calculations. Our theoretical calculations indicate that in contrast to bulk black P, the SL and DL black/blue P can maintain the layered structures during lithiated and delithiated process. Also their diffusion energy barriers are smaller than those of graphene and silicene. Further studies indicate that DL black P, SL and DL blue P may have high charge capacities. All of these characteristics suggest that the 2D black and blue P are potential candidates for anode materials of LIBs. Note. When finalizing our work, we became aware of a recent study by Zhao et al.[50], in which the authors also predict layered black P is a possible potential candidate for anode materials of LIBs, agreeing with our conclusion.

Acknowledgements

The work was supported by National Key Project for Basic Research of China (Grants No. 2011CB922101, 2014CB921104, 2013CB922301), China Postdoctoral Science Foundation (2014M551544), NSFC( Grants No. 11374137, 61125403, 11105075,11274177,11447192), PAPD and National Science Council of Taiwan (NSC98-2113M-001-029-MY3 and NSC101-2113-M-001-023-MY3) Academia Sinica 10804053.



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FIG. 1: Top and side views of black and blue phosphorus. (a) Single-layer (SL) black P with 2 × 2 supercell; (b) SL blue P with 3 × 3 supercell; (c)Double-layer (DL) black P with 2 × 2 supercell; (d) DL blue P with 3 × 3 supercell.



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FIG. 2: Optimized structures of lithiated SL black and blue P ( Lix P1−x ). The 2 × 2 supercell in black P and 3 × 3 supercell in blue P are outlined in top view.


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FIG. 3: Optimized structures of lithiated double-layer black and blue P. The 2 × 2 supercell in black P and 3 × 3 supercell in blue P are outlined in top view.

FIG. 4: Adsorption energy as the function of Li concentration, x, for SL and DL black and blue P, Lix P1−x .



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FIG. 5: ELF contour plot around Li. (a) Single-layer black P with one Li adatom, and (b)Single-layer blue P with one Li adatom. P1, P2 and P3 are the three nearest neighbor P atoms of Li

FIG. 6: Density of states of single-layer and double-layer black/blue P without Li adsorption and with the lowest and highest Li adsorption concentration


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FIG. 7: Schematic representations and potential-energy curves of Li diffusion on single-layer black and blue P.



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FIG. 8: Schematic representations and potential-energy curves of Li diffusion: (a) in the direction perpendicular to the black phosphorus sheet, (b) in the direction perpendicular to the blue phosphorus sheet, (c) on the surface of single-layer black P at high concentration and (d) on the surface of single-layer blue P at high concentration. The initial (i), intermediate (m) and final (f) states are illustrated on the right side. Red circle represents the diffusion atom.


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FIG. 9: Potential-energy curves of Li diffusion on DL black and blue P at low concentration (panels a and b) and high concentration (panels c and d). Schematic representations of diffusion paths are shown in the figure.



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FIG. 10: Table of contents graphic


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Theoretical Prediction of Anode Materials in Li-Ion Batteries on

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