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Ultrafast and Directional Diffusion of Lithium in Phosphorene for High-Performance Lithium-Ion Battery Weifeng Li, Yanmei Yang, Gang Zhang, and Yong-Wei Zhang Nano Lett., Just Accepted Manuscript • DOI: 10.1021/nl504336h • Publication Date (Web): 09 Feb 2015 Downloaded from http://pubs.acs.org on February 12, 2015
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Ultrafast and Directional Diffusion of Lithium in Phosphorene for HighPerformance Lithium-Ion Battery Weifeng Li1, Yanmei Yang2, Gang Zhang*1, Yong-Wei Zhang*1 1. Institute of High Performance Computing, A*STAR, Singapore, 138632 2. School for Radiological and Interdisciplinary Sciences (RAD-X) & Collaborative Innovation Center of Radiation Medicine of Jiangsu Higher Education Institutions, Soochow University, Suzhou, China, 215123 E-mail: [email protected]; [email protected] Abstract Density functional theory calculations have been performed to investigate the binding and diffusion behaviour of Li in phosphorene. Our studies reveal the following findings: 1). Li atom forms strong binding with phosphorus atoms and exists in the cationic state; 2) the shallow energy barrier (0.08 eV) of Li diffusion on monolayer phosphorene along zigzag direction leads to an ultrahigh diffusivity, which is estimated to be 102 (104) times faster than that on MoS2 (graphene) at room temperature; 3) the large energy barrier (0.68 eV) along armchair direction results in a nearly forbidden diffusion, and such strong diffusion anisotropy is absent in graphene and MoS2; 4) a remarkably large average voltage of 2.9 V is predicted in the phosphorene-based Li-ion battery; and 5) a semiconducting to metallic transition induced by
Li intercalation of phosphorene gives rise to a good electrical
conductivity, ideal for use as an electrode. Given these advantages, it is expected that phosphorene will present abundant opportunities for applications in novel electronic device and lithium-ion battery with a high rate capability and high charging voltage. Keywords: Phosphorene, Lithium adsorption, Directional diffusion, Lithium Battery
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1. Introduction With the rapid development of consumer electronics such as mobile devices and electric vehicles, rechargeable battery with high capacity and rate capacity has attracted great attention from both basic research and industry applications. Lithium ion battery (Li-Battery), one of the most widely studied rechargeable batteries, is a critical enabler for the next generation energy technology due to its advantages in portability and energy efficiency.1-3 The growing interest in Li-Battery has greatly accelerated the development of electrode materials. Recently, novel architectures using two dimensional (2D) nanomaterials have been widely explored. For example, graphene, the most well-studied 2D material, exhibits unique capacity in Li-Battery because of its high charge carrier mobility,4 large surface area5 and a broad electrochemical window.6 Up to date, graphene has been utilized as both anode and cathode materials with great success.7-15 Molybdenum disulfide (MoS2), another typical layered material, has also been demonstrated as an ideal anode material for Li-Battery
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and exhibits a high reversible lithium storage capacity and superior rate capability. Since 2007, black phosphorus (the most-stable form of the bulk phosphorus) and red phosphorus have received much interest due to its potential as a high-performance anode material in Li-Battery.20-30 By incorporating carbon into black phosphorus, it was demonstrated that the capacity of Li-Battery was able to reach 2786 mAh·g-1 with an excellent cyclic life of 100 cycles and 80% capacity retention.30 Very recently, a new 2D material, phosphorene, has been successfully isolated from black phosphorus.31-33 The phosphorene monolayer consists of P atoms stacked in puckered sub-planes. Each P atom is bonded with two adjacent atoms lying in the same plane and with one P atom from a different plane. Black phosphorene, the bulk form, can be formed by stacking phosphorene monolayer through weak inter-layer van der Waals (vdW) interaction with an interlayer distance of 3.09 Å. Then, an interesting question arises naturally and promptly: Is monolayer phosphorene a
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promising anode material for Li-Battery? To answer this question, a detailed study on the Li adsorption and diffusion process in monolayer phosphorene is indispensible. Here, we report our theoretical studies of the adsorption and diffusion of Li atom in both phosphorene and black phosphorus. Our studies show that Li atoms are able to intercalate with phosphorus atoms with a binding energy of around -1.9 eV, indicating a strong interaction between two elements. Li exists in cationic state with its 2s1 electron being completely transferred to phosphorus. Modulated by its puckered structure, Li diffusion in phosphorene shows a strong directional anisotropy: along the zigzag direction, the migration barrier is only 0.08 eV for Li on phosphorene surface; while for the armchair direction, the barrier is 0.68 eV. The extremely small energy barrier along the zigzag direction guarantees rapid diffusion of Li atoms, with diffusivity being estimated to be 102~104 times faster than other 2D anode candidates, like graphene and MoS2. Moreover, the average voltage of the Li intercalation with phosphorene is estimated to be 2.9 V, which is higher than other types of commercial anode materials. Based on our present findings, phosphorene and black phosphorus are expected to be used in novel electronic device and Li-Battery with a high rate capacity and high open circuit voltage.
2. Computational Details All the calculations were performed using Vienna ab initio simulation package (VASP).34, 35 Projector-augmented-wave (PAW) potentials36 were used to take into account the electron-ion interactions, while the electron exchange-correlation interactions were treated using generalized gradient approximation (GGA)37 in the scheme of Perdew-BurkeErnzerhof. A plane wave cutoff of 500 eV was used for all the calculations. All atomic positions and lattice vectors (monolayer bulk) were fully optimized using a conjugate gradient algorithm to obtain the unstrained configuration. Atomic relaxation was performed
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until the change of total energy was less than 0.01 meV and all the forces on each atom were smaller than 0.01 eV/Å. For the Li adsorption and diffusion studies, the supercell contains 4 × 3 primitive cells of phosphorene, which results in a Li/P ratio of 0.021. For the monolayer phosphorene, a vacuum space of 20 Å was placed between adjacent layers to avoid mirror interactions. K-point samplings of 5 × 5 × 1 (monolayer phosphorene) and 5 × 5 × 5 (bulk black phosphorus) were used for the structure relaxation, while denser meshes of 15 × 15 × 1 (monolayer) and 15 × 15 × 15 (bulk) were used to calculate energies and band structures. For Li diffusion in phosphorene/black phosphorus, we also performed minimum energy path profiling using the climbing image nudged elastic band method as implemented in the VASP transition state tools.38, 39 The structural convergence criteria were similar to that used in the above-mentioned structure optimization.
3. Results and Discussion 3.1 Adsorption of Li on phosphorene surface As an electrode material, it is essential for monolayer phosphorene to attract Li with relatively strong binding energy. As illustrated in Fig. 1a, the Li atoms are first loaded to phosphorene surface, then diffuse along armchair or ziagzag direction on the surface. As a consequence, we first examine the surface loading (adsorption process) of Li atom on phosphorene surface. We have explored the phosphorene surface for Li binding by placing one Li atom at different sites above phosphorene before structural optimization, and found that the most stable binding site is above the groove between two P “slifftops” as shown in the inserts of Fig. 1b. Specifically, the distance between Li and P1 atom is 2.47 Å, and the distances betewen Li and P2/P3 atoms are 2.56 Å. Then we move the Li atom vertically away from the phosphorene surface, with the distance to phosphorene surface from 0.15 nm (the most stable binding site) to about 1 nm. The change of potential energy with respect to Li-
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phosphorene surface distance is shown in Fig. 1b. For distance larger than 8 Å, the energy is almost kept constant. This means that, beyond 8 Å, the total energy of the complex system does not change because Li has no interactions with phosphorene, which can be treated as isolated Li atom and phosphorene sheet. Within 6 Å, however, the energy decreases dramatically, indicating strong interaction between Li and phosphorus atoms. It is clear that there is no energy barrier in the Li loading process. The binding energy ( ) can be evaluated as follows : = − −
(1)
where , and are the total energies of Li-adsorbed phosphorene, phosphorene layer and a Li atom, respectively. According to this definition, a more negative value of indicates a more energetically favorable (exothermic) reaction. From our calculation, the value of for Li on monolayer phosphorene is -1.97 eV, which granartees a rapid loading process and strong binding between the phosphorus atoms and Li. The spatial distribution of the charge difference between Li and phosphorene is illustrated in Fig. 1c. The large charge deficiency at Li and charge excess around nearby P atoms indicate strong electron transfer from Li to phosphorene. According to Bader charge population analysis,40 Li possesses a unit positive charge with its 2s1 electron being completely transferred to phosphorene, and thus exists in the cationic state.
3.2 Diffusion of Li on phosphorene surface The charging and circuit rate performance of the Li-Battery is mainly determined by the Li mobility on the electrode material. It is desirable to quantify the diffusion of Li atom on the surface of phosphorene. Being distinct from the sp2 hybridization of C atoms in graphene, the phosphorene has a puckered structure, with its atoms arranged in a honeycomb lattice from top view as shown in Fig. 1a. This structural anisotropy plays an important role in the
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migration of Li atom on its surface. As illustrated in Fig. 2b and 2d, considering the symmetry of the primitive cell, we have selected two representative diffusive pathways: one is path B1-S1-B3, which is along the armchair direction; the other is the path B1-S2-B2-S3B3, which is along the zigzag direction, as shown in Fig. 2b-e. The energy profiles along armchair and zigzag directions are summarized in Fig. 2a. For the case of Li diffusion along armchair direction (red line in Fig. 2a), there is only one peak of 0.68 eV. On the contrary, for the diffusion along zigzag direction (black line in Fig. 2a), a rather small berrier of 0.08 eV is found. The temperature-dependent molecular transition rate can41-44 be evaluated by the arrhenius equation, from which the diffusion constant (D) of Li follows: ~− ⁄
(2)
where and are the activation energy (diffusion barrier) and Boltzmann’s constant, T is the environmental temperature. According to Eq. 2, the diffusion mobility of Li along ziagzag direction on phosphorene surface is about 1010 faster than that along armchair direction at room temperature, indicating that without an external electrical field, the large energy barrier (0.68 eV) along armchair direction essentially prevents Li diffusion along this direction at room temperature. Along armchair diffusion path, the binding position corresponding to the saddle point labelled as S1 is at the top of a P atom as shown in Fig. 2. Hence the high diffusion barrier is due to the phosphorus “slifftop” between two adjcent grooves which makes the Li diffusion extremely difficult. The remakably quasi-one-dimensional diffusion observed in monolayer phosphorene is clearly absent in other 2D materials. For instance, the Li diffusion in MoS2, VS2 and graphene are essentially isotropic in the plane, with the values of diffusion barrier being 0.25 eV on MoS2,42 0.22 eV on VS2,42 0.327 eV on graphene44 which are much larger than that along the zigzag direction on phosphorene. Remarkably, at room temperature, the Li diffusion mobility on phosphorene (zigzag direction) is estimated to
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be 7.2×102/1.4×104 times faster than that on MoS2 and graphene, respectively. Therefore, an extremely high-rate capability is expected for phosphorene-based Li-Battery.
3.3 Diffusion of Li inside black phosphorus interior It is necessary to compare the diffusion behavior in monolayer phosphorene with that in its bulk counterpart, that is, black phosphorus. For black phosphorus, we used the ABstacking crystal structure, which is energetically the most favorable.45 As shown in Fig. 3b-e, the Li’s stable site relative to the bottom layer (layer 1 in Fig. 3c) is similar to that on phosphorene: right above the groove. For AB-stacking order as shown in Fig. 3b and 3d, the groove of the top layer (layer 2 in Fig. 3c) is located right above Li atom. Compared to the monolayer phosphorene, the additional interactions from both side in the black phosphorus results in a stronger binding energy, = -2.24 eV. The energy profiles for Li diffusion inside black phosphorus connecting two adjcent binding sites are summarized in Fig. 3a. Compared to the monolayer phosphorene, one distinct characteristic is that the energy profile representating armchair diffusion has two energy barriers. This is because the existance of the layer 2 in Fig. 3c provides another binding site (B2) for Li diffusion. Another distinct characteristic is the lowered energy barriers for Li diffusion along both armchair and zigzag directions. Although the Li diffusion barrier along zigzag direction reduces slightly from 0.08 eV (monolayer phosphorene) to 0.05 eV (black phosphorus), there is a remarkable reduction along the armchair direction from 0.68 eV to 0.20 eV. Thus the significant quasi-one-dimensional diffusion path in monolayer phosphorene weakens in its bulk counterpart, arising from the additional interactions with the adjacent layer.
3.4 Effect of Li concentration and theoretical voltage profile Open-circuit-voltage data is widely used for characterizing the performance of Li-battery, 7 ACS Paragon Plus Environment
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such as state-of-charge and state-of-health. In theory, the open circuit voltage curve can be obtained by calculating the average voltage over parts of the Li composition domain. 46-48 The average voltage of LixP in the range of x1 ≤ x ≤ x2 is given as: ≈
!"#$ % !"& $ ' & % # ! & % #
(3)
where "# , "& and are the energy of Lix1P, Lix2P and metallic Li, respectively. Based on this method, by screening a series of Li/P ratios (x values), a variety of properties pertinent to Li-batteries can be predicted and shown to be accurate, such as the average insertion potential46-50 and the charge/discharge voltage profiles of Li intercalation in metal oxides and metal dichalcogenides51-53. In this work, we consider a series of higher configurations with stoichiometry of LixP (x = 0.042, 0.083, 0.125 and 0.25) as shown in Fig. 4a-d, with one Li atom binded on one side of a 3 × 2, 3 × 1, 1 × 2 and 1 × 1 supercell, respectively. For most of the concentrations (Fig. 4e), Li has a binding energy lower than -1.9 eV. On the contrary, for one Li in one (1 × 1) primitive cell (x = 0.25), weaker binding is observed with a binding energy of -1.70 eV, indicating that the complex becomes less stable due to the pronounced electrostatic repulsive interactions between adjacent Li cations. Higher concentrations of Li insertion into phosphorene (two Li atoms in one primitive cell, x = 0.5) will cause P-P bond breaking, which disrupts the layer structure. As indicated in the recent experiment30, the breaking of PP bonds cannot be rebuilt and hence the lithiation/delithiation process becomes irreversible. As a consequence, only low Li concentrations ( 0 < x ≤ 0.25 ) are considered in the current work. The voltage profile with respect to Li content is shown in Fig. 5. Generally, there is a dramatic drop from 3.7 V when x < 0.05. Then the voltage profile becomes a gently sloping curve. The calculated average voltage by numercally averaging the voltage profile is 2.9 V (0 ≤ x ≤ 0.25), which is obviously higher than those of graphite42 and TiO2 electrode54, for 8 ACS Paragon Plus Environment
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which the average voltage is around 1.5V. Thus the phosphorene-based Li-battery is able to provide a much higher charging voltage, which cannot be achieved by exising anode materials. For the case of Li binding in black phosphorus interior (the bulk), we have also considered a series of Li concentrations. In the calculations, two Li atoms were placed in black phosphorus with supercell sizes of 4 × 3, 3 × 2, 3 × 1, 1 × 2 and 1 × 1, which correspond to Li/P ratios of 0.021, 0.042, 0.083, 0.125 and 0.25, respectively. As stacking of the adjacent phosphorus layers affects the Li binding position with respect to its neighbours, we have considered four distributions of the two Li atoms in each model. As illustrated in Fig. 6, taking the 4 × 3 supercell model for example, the first Li atom is always on position 0 (on top of layer 1), the other Li atom has four positions, that is, positions 1 - 4, on top of layer 2. Specifically, position 1 is directly on the top of position 0, position 2 is obtained by shifting half lattice vector length along b direction from position 1, position 3 is obtained by shifting half lattice vector length along a direction from position 1, and position 4 is obtained by shifting half lattice vector length along both the a and b directions from position 1. In general, position 4 represents the full dispersed distribution of Li stacking. The binding energies for the four Li configurations are summarized in Fig. 6d. At low Li concentration, the fully dispersed distribution (one Li on position 0 and the other one on position 4) has the lowest binding energy. This reflects the fact that Li atoms prefer to disperse in the phosphorus bulk. As Li concentration increases, the difference in the binding energy for different Li distributions becomes smaller and vanishes at around x=0.1. Moreover, the absolute values of the binding energy decrease quickly with increasing Li content, which is similar to the case of Li adsorption on phosphorene surface as illustrated in Fig. 4e. The average voltage for bulk phosphorus is predicted to be 1.7 V. This value is slightly larger than but still qualitatively consistent with the experimental measurement, which is around 0.9-
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1.2V for black phosphorus20, 30. It is interesting to find that the average voltage is 2.9 V (0 ≤ x ≤ 0.25) for monolayer phosphorene, which is obviously higher than that of bulk black phosphorus within the same Li content. Thus the phosphorene-based Li-battery is expected to provide a much higher charging voltage. 46-48
3.5 Electronic property of phosphorene intercalated with Li Consider the fact that Li-batteries have been used to power an increasing diverse range of applications, such as low-current cells used for portable electronics and memory backup and also high-current cells used in military applications, it is essential to understand the electronic properties of electrode materials with resepct to their battery performance. Different from graphene, monolayer phosphorene has a low electronic conductivity because of its semiconducting characteristic with finite bandgap as shown in Fig. 7a.32, 33, 55 Hence, it is essential to examine the electronic properties of phosphorene with Li intercalation. The electronic band structure of phosphorene with Li adsorption at Li0.02P is shown in Fig. 7b. From Bader charge analysis56, the 2s1 electron of Li is completely transferred to phosphorene, which effectively shifts the Fermi energy level into the original conduction band. Hence the complex system has changed from “semiconducting” to “metallic” with considerable electronic states at the Fermi energy level. For the case of lowest Li concentration, Li0.02P, there is one band crossing the Fermi level. The electron distribution correlated to this band is illustrated in Fig. 7c, which is spreading only along the armchair direction and forming the electron conducting channel. However, for larger Li concentration like Li0.042P, the conducting electron spreads in the whole phosphorene layer, displaying less direction dependence as shown in Fig. 7d.
4. Conclusion
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To conclude, by performing density functional theories calculations, we have analysed the Li adsorption and diffusion in phosphorene monolayer and also inside the bulk. Our studies show that Li atom is able to form stable adsorption with phosphorus atoms with a binding energy around -1.9 eV. Upon adsorption, Li denotes its 2s1 electron to phosphorus and exists in the cationic state. The adsorbed complex becomes metallic, which is essential for use as an electrode. Modulated by its puckered structure, the diffusion of Li on phosphorene is highly anisotropic, with diffusion along the zigzag direction being highly energetically favourable, while diffusion along the armchair direction is almost prohibited. Specifically, the energy barrier along the zigzag direction is only 0.08 eV for Li in monolayer phosphorene, much lower than that in two other Li-Battery anode candidates, graphene and MoS2. Furthermore, the average voltage of the Li intercalation is estimated to be 2.9 V, suitable for high charging voltage applications. Based on our present findings, monolayer phosphorene is expected to be used in novel electronic device and Li-Battery with a high charging voltage and high rate capability.
Acknowledgement This work was supported by the A*STAR Computational Resource Centre through the use of its high performance computing facilities, the National Natural Science Foundation of China (grant no. 11304214) and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).
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47.
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Figure 1. (a) Schematic of Li surface loading (adsorption process), diffusion along armchair and zigzag directions on phosphorene surface; (b) total potential energy of Li on phosphorene surface with respect to Li-phosphorene distance and (c) charge density difference between Li and phosphorene, indicating electron transfer from Li to phosphorene.
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Figure 2. (a) Energy profiles of Li diffusion along armchair and zigzag directions on phosphorene surface (S1, S2 and S3 denote the saddle points; B1, B2 and B3 denote the binding sites); (b), (c) top view and side view of Li diffusion pathway along the armchair direction; (d), (e) top view and side view of Li diffusion pathway along the zigzag direction.
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Figure 3. (a) Energy profiles of Li diffusion along armchair and zigzag directions in black phosphorus (S1 and S2 denote the saddle points; B1, B2 and B3 denote the binding sites); (b), (c) Top view and side view of Li diffusion pathway along the armchair direction, S1 indicates the Li position at the saddle point; (d), (e) Top view and side view of Li diffusion pathway along the zigzag direction, S2 indicates the Li position at the saddle point.
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Figure 4. (a-d) Configutations of schematics of LixP with Li binded on one side of phosphorene; and (e) binding energies with increasing Li content.
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Figure 5. Calculated voltage profile with respect to Li content from 0 to 0.25.
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Figure 6. (a-c) Binding positions of two Li atoms distributed in a 4 × 3 black phosphorus supercell: First Li is always on position 0 on top of layer 1, second Li can be on positions 1-4 on top of layer 2. In detail, position 1 is on the top of position 0, position 2 is obtained by shifting half lattice vector length from position 1 along b direction, position 3 is obtained by shifting half lattice vector length along a direction, and position 4 is obtained by shifting half lattice vector length along both the a and b directions. (d) binding energies with increasing Li content.
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Figure 7. Electronic band structures of (a) pristine phosphorene and (b) phosphorene with Li intercalation. The blue-colored dash lines indicate the Fermi energy level. Electron density distributions of the bands crossing the Fermi energy level of system (c) Li0.02P and (d) Li0.042P (isosurface = 0.0007|e|/bohr3).
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Ultrafast and Directional Diffusion of Lithium in Phosphorene for High-Performance Lithium-Ion Battery Weifeng Li, Yanmei Yang, Gang Zhang, and Yong-Wei Zhang Nano Lett., Just Accepted Manuscript • DOI: 10.1021/nl504336h • Publication Date (Web): 09 Feb 2015 Downloaded from http://pubs.acs.org on February 12, 2015
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Ultrafast and Directional Diffusion of Lithium in Phosphorene for HighPerformance Lithium-Ion Battery Weifeng Li1, Yanmei Yang2, Gang Zhang*1, Yong-Wei Zhang*1 1. Institute of High Performance Computing, A*STAR, Singapore, 138632 2. School for Radiological and Interdisciplinary Sciences (RAD-X) & Collaborative Innovation Center of Radiation Medicine of Jiangsu Higher Education Institutions, Soochow University, Suzhou, China, 215123 E-mail: [email protected]; [email protected] Abstract Density functional theory calculations have been performed to investigate the binding and diffusion behaviour of Li in phosphorene. Our studies reveal the following findings: 1). Li atom forms strong binding with phosphorus atoms and exists in the cationic state; 2) the shallow energy barrier (0.08 eV) of Li diffusion on monolayer phosphorene along zigzag direction leads to an ultrahigh diffusivity, which is estimated to be 102 (104) times faster than that on MoS2 (graphene) at room temperature; 3) the large energy barrier (0.68 eV) along armchair direction results in a nearly forbidden diffusion, and such strong diffusion anisotropy is absent in graphene and MoS2; 4) a remarkably large average voltage of 2.9 V is predicted in the phosphorene-based Li-ion battery; and 5) a semiconducting to metallic transition induced by
Li intercalation of phosphorene gives rise to a good electrical
conductivity, ideal for use as an electrode. Given these advantages, it is expected that phosphorene will present abundant opportunities for applications in novel electronic device and lithium-ion battery with a high rate capability and high charging voltage. Keywords: Phosphorene, Lithium adsorption, Directional diffusion, Lithium Battery
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1. Introduction With the rapid development of consumer electronics such as mobile devices and electric vehicles, rechargeable battery with high capacity and rate capacity has attracted great attention from both basic research and industry applications. Lithium ion battery (Li-Battery), one of the most widely studied rechargeable batteries, is a critical enabler for the next generation energy technology due to its advantages in portability and energy efficiency.1-3 The growing interest in Li-Battery has greatly accelerated the development of electrode materials. Recently, novel architectures using two dimensional (2D) nanomaterials have been widely explored. For example, graphene, the most well-studied 2D material, exhibits unique capacity in Li-Battery because of its high charge carrier mobility,4 large surface area5 and a broad electrochemical window.6 Up to date, graphene has been utilized as both anode and cathode materials with great success.7-15 Molybdenum disulfide (MoS2), another typical layered material, has also been demonstrated as an ideal anode material for Li-Battery
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and exhibits a high reversible lithium storage capacity and superior rate capability. Since 2007, black phosphorus (the most-stable form of the bulk phosphorus) and red phosphorus have received much interest due to its potential as a high-performance anode material in Li-Battery.20-30 By incorporating carbon into black phosphorus, it was demonstrated that the capacity of Li-Battery was able to reach 2786 mAh·g-1 with an excellent cyclic life of 100 cycles and 80% capacity retention.30 Very recently, a new 2D material, phosphorene, has been successfully isolated from black phosphorus.31-33 The phosphorene monolayer consists of P atoms stacked in puckered sub-planes. Each P atom is bonded with two adjacent atoms lying in the same plane and with one P atom from a different plane. Black phosphorene, the bulk form, can be formed by stacking phosphorene monolayer through weak inter-layer van der Waals (vdW) interaction with an interlayer distance of 3.09 Å. Then, an interesting question arises naturally and promptly: Is monolayer phosphorene a
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promising anode material for Li-Battery? To answer this question, a detailed study on the Li adsorption and diffusion process in monolayer phosphorene is indispensible. Here, we report our theoretical studies of the adsorption and diffusion of Li atom in both phosphorene and black phosphorus. Our studies show that Li atoms are able to intercalate with phosphorus atoms with a binding energy of around -1.9 eV, indicating a strong interaction between two elements. Li exists in cationic state with its 2s1 electron being completely transferred to phosphorus. Modulated by its puckered structure, Li diffusion in phosphorene shows a strong directional anisotropy: along the zigzag direction, the migration barrier is only 0.08 eV for Li on phosphorene surface; while for the armchair direction, the barrier is 0.68 eV. The extremely small energy barrier along the zigzag direction guarantees rapid diffusion of Li atoms, with diffusivity being estimated to be 102~104 times faster than other 2D anode candidates, like graphene and MoS2. Moreover, the average voltage of the Li intercalation with phosphorene is estimated to be 2.9 V, which is higher than other types of commercial anode materials. Based on our present findings, phosphorene and black phosphorus are expected to be used in novel electronic device and Li-Battery with a high rate capacity and high open circuit voltage.
2. Computational Details All the calculations were performed using Vienna ab initio simulation package (VASP).34, 35 Projector-augmented-wave (PAW) potentials36 were used to take into account the electron-ion interactions, while the electron exchange-correlation interactions were treated using generalized gradient approximation (GGA)37 in the scheme of Perdew-BurkeErnzerhof. A plane wave cutoff of 500 eV was used for all the calculations. All atomic positions and lattice vectors (monolayer bulk) were fully optimized using a conjugate gradient algorithm to obtain the unstrained configuration. Atomic relaxation was performed
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until the change of total energy was less than 0.01 meV and all the forces on each atom were smaller than 0.01 eV/Å. For the Li adsorption and diffusion studies, the supercell contains 4 × 3 primitive cells of phosphorene, which results in a Li/P ratio of 0.021. For the monolayer phosphorene, a vacuum space of 20 Å was placed between adjacent layers to avoid mirror interactions. K-point samplings of 5 × 5 × 1 (monolayer phosphorene) and 5 × 5 × 5 (bulk black phosphorus) were used for the structure relaxation, while denser meshes of 15 × 15 × 1 (monolayer) and 15 × 15 × 15 (bulk) were used to calculate energies and band structures. For Li diffusion in phosphorene/black phosphorus, we also performed minimum energy path profiling using the climbing image nudged elastic band method as implemented in the VASP transition state tools.38, 39 The structural convergence criteria were similar to that used in the above-mentioned structure optimization.
3. Results and Discussion 3.1 Adsorption of Li on phosphorene surface As an electrode material, it is essential for monolayer phosphorene to attract Li with relatively strong binding energy. As illustrated in Fig. 1a, the Li atoms are first loaded to phosphorene surface, then diffuse along armchair or ziagzag direction on the surface. As a consequence, we first examine the surface loading (adsorption process) of Li atom on phosphorene surface. We have explored the phosphorene surface for Li binding by placing one Li atom at different sites above phosphorene before structural optimization, and found that the most stable binding site is above the groove between two P “slifftops” as shown in the inserts of Fig. 1b. Specifically, the distance between Li and P1 atom is 2.47 Å, and the distances betewen Li and P2/P3 atoms are 2.56 Å. Then we move the Li atom vertically away from the phosphorene surface, with the distance to phosphorene surface from 0.15 nm (the most stable binding site) to about 1 nm. The change of potential energy with respect to Li-
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phosphorene surface distance is shown in Fig. 1b. For distance larger than 8 Å, the energy is almost kept constant. This means that, beyond 8 Å, the total energy of the complex system does not change because Li has no interactions with phosphorene, which can be treated as isolated Li atom and phosphorene sheet. Within 6 Å, however, the energy decreases dramatically, indicating strong interaction between Li and phosphorus atoms. It is clear that there is no energy barrier in the Li loading process. The binding energy ( ) can be evaluated as follows : = − −
(1)
where , and are the total energies of Li-adsorbed phosphorene, phosphorene layer and a Li atom, respectively. According to this definition, a more negative value of indicates a more energetically favorable (exothermic) reaction. From our calculation, the value of for Li on monolayer phosphorene is -1.97 eV, which granartees a rapid loading process and strong binding between the phosphorus atoms and Li. The spatial distribution of the charge difference between Li and phosphorene is illustrated in Fig. 1c. The large charge deficiency at Li and charge excess around nearby P atoms indicate strong electron transfer from Li to phosphorene. According to Bader charge population analysis,40 Li possesses a unit positive charge with its 2s1 electron being completely transferred to phosphorene, and thus exists in the cationic state.
3.2 Diffusion of Li on phosphorene surface The charging and circuit rate performance of the Li-Battery is mainly determined by the Li mobility on the electrode material. It is desirable to quantify the diffusion of Li atom on the surface of phosphorene. Being distinct from the sp2 hybridization of C atoms in graphene, the phosphorene has a puckered structure, with its atoms arranged in a honeycomb lattice from top view as shown in Fig. 1a. This structural anisotropy plays an important role in the
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migration of Li atom on its surface. As illustrated in Fig. 2b and 2d, considering the symmetry of the primitive cell, we have selected two representative diffusive pathways: one is path B1-S1-B3, which is along the armchair direction; the other is the path B1-S2-B2-S3B3, which is along the zigzag direction, as shown in Fig. 2b-e. The energy profiles along armchair and zigzag directions are summarized in Fig. 2a. For the case of Li diffusion along armchair direction (red line in Fig. 2a), there is only one peak of 0.68 eV. On the contrary, for the diffusion along zigzag direction (black line in Fig. 2a), a rather small berrier of 0.08 eV is found. The temperature-dependent molecular transition rate can41-44 be evaluated by the arrhenius equation, from which the diffusion constant (D) of Li follows: ~− ⁄
(2)
where and are the activation energy (diffusion barrier) and Boltzmann’s constant, T is the environmental temperature. According to Eq. 2, the diffusion mobility of Li along ziagzag direction on phosphorene surface is about 1010 faster than that along armchair direction at room temperature, indicating that without an external electrical field, the large energy barrier (0.68 eV) along armchair direction essentially prevents Li diffusion along this direction at room temperature. Along armchair diffusion path, the binding position corresponding to the saddle point labelled as S1 is at the top of a P atom as shown in Fig. 2. Hence the high diffusion barrier is due to the phosphorus “slifftop” between two adjcent grooves which makes the Li diffusion extremely difficult. The remakably quasi-one-dimensional diffusion observed in monolayer phosphorene is clearly absent in other 2D materials. For instance, the Li diffusion in MoS2, VS2 and graphene are essentially isotropic in the plane, with the values of diffusion barrier being 0.25 eV on MoS2,42 0.22 eV on VS2,42 0.327 eV on graphene44 which are much larger than that along the zigzag direction on phosphorene. Remarkably, at room temperature, the Li diffusion mobility on phosphorene (zigzag direction) is estimated to
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be 7.2×102/1.4×104 times faster than that on MoS2 and graphene, respectively. Therefore, an extremely high-rate capability is expected for phosphorene-based Li-Battery.
3.3 Diffusion of Li inside black phosphorus interior It is necessary to compare the diffusion behavior in monolayer phosphorene with that in its bulk counterpart, that is, black phosphorus. For black phosphorus, we used the ABstacking crystal structure, which is energetically the most favorable.45 As shown in Fig. 3b-e, the Li’s stable site relative to the bottom layer (layer 1 in Fig. 3c) is similar to that on phosphorene: right above the groove. For AB-stacking order as shown in Fig. 3b and 3d, the groove of the top layer (layer 2 in Fig. 3c) is located right above Li atom. Compared to the monolayer phosphorene, the additional interactions from both side in the black phosphorus results in a stronger binding energy, = -2.24 eV. The energy profiles for Li diffusion inside black phosphorus connecting two adjcent binding sites are summarized in Fig. 3a. Compared to the monolayer phosphorene, one distinct characteristic is that the energy profile representating armchair diffusion has two energy barriers. This is because the existance of the layer 2 in Fig. 3c provides another binding site (B2) for Li diffusion. Another distinct characteristic is the lowered energy barriers for Li diffusion along both armchair and zigzag directions. Although the Li diffusion barrier along zigzag direction reduces slightly from 0.08 eV (monolayer phosphorene) to 0.05 eV (black phosphorus), there is a remarkable reduction along the armchair direction from 0.68 eV to 0.20 eV. Thus the significant quasi-one-dimensional diffusion path in monolayer phosphorene weakens in its bulk counterpart, arising from the additional interactions with the adjacent layer.
3.4 Effect of Li concentration and theoretical voltage profile Open-circuit-voltage data is widely used for characterizing the performance of Li-battery, 7 ACS Paragon Plus Environment
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such as state-of-charge and state-of-health. In theory, the open circuit voltage curve can be obtained by calculating the average voltage over parts of the Li composition domain. 46-48 The average voltage of LixP in the range of x1 ≤ x ≤ x2 is given as: ≈
!"#$ % !"& $ ' & % # ! & % #
(3)
where "# , "& and are the energy of Lix1P, Lix2P and metallic Li, respectively. Based on this method, by screening a series of Li/P ratios (x values), a variety of properties pertinent to Li-batteries can be predicted and shown to be accurate, such as the average insertion potential46-50 and the charge/discharge voltage profiles of Li intercalation in metal oxides and metal dichalcogenides51-53. In this work, we consider a series of higher configurations with stoichiometry of LixP (x = 0.042, 0.083, 0.125 and 0.25) as shown in Fig. 4a-d, with one Li atom binded on one side of a 3 × 2, 3 × 1, 1 × 2 and 1 × 1 supercell, respectively. For most of the concentrations (Fig. 4e), Li has a binding energy lower than -1.9 eV. On the contrary, for one Li in one (1 × 1) primitive cell (x = 0.25), weaker binding is observed with a binding energy of -1.70 eV, indicating that the complex becomes less stable due to the pronounced electrostatic repulsive interactions between adjacent Li cations. Higher concentrations of Li insertion into phosphorene (two Li atoms in one primitive cell, x = 0.5) will cause P-P bond breaking, which disrupts the layer structure. As indicated in the recent experiment30, the breaking of PP bonds cannot be rebuilt and hence the lithiation/delithiation process becomes irreversible. As a consequence, only low Li concentrations ( 0 < x ≤ 0.25 ) are considered in the current work. The voltage profile with respect to Li content is shown in Fig. 5. Generally, there is a dramatic drop from 3.7 V when x < 0.05. Then the voltage profile becomes a gently sloping curve. The calculated average voltage by numercally averaging the voltage profile is 2.9 V (0 ≤ x ≤ 0.25), which is obviously higher than those of graphite42 and TiO2 electrode54, for 8 ACS Paragon Plus Environment
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which the average voltage is around 1.5V. Thus the phosphorene-based Li-battery is able to provide a much higher charging voltage, which cannot be achieved by exising anode materials. For the case of Li binding in black phosphorus interior (the bulk), we have also considered a series of Li concentrations. In the calculations, two Li atoms were placed in black phosphorus with supercell sizes of 4 × 3, 3 × 2, 3 × 1, 1 × 2 and 1 × 1, which correspond to Li/P ratios of 0.021, 0.042, 0.083, 0.125 and 0.25, respectively. As stacking of the adjacent phosphorus layers affects the Li binding position with respect to its neighbours, we have considered four distributions of the two Li atoms in each model. As illustrated in Fig. 6, taking the 4 × 3 supercell model for example, the first Li atom is always on position 0 (on top of layer 1), the other Li atom has four positions, that is, positions 1 - 4, on top of layer 2. Specifically, position 1 is directly on the top of position 0, position 2 is obtained by shifting half lattice vector length along b direction from position 1, position 3 is obtained by shifting half lattice vector length along a direction from position 1, and position 4 is obtained by shifting half lattice vector length along both the a and b directions from position 1. In general, position 4 represents the full dispersed distribution of Li stacking. The binding energies for the four Li configurations are summarized in Fig. 6d. At low Li concentration, the fully dispersed distribution (one Li on position 0 and the other one on position 4) has the lowest binding energy. This reflects the fact that Li atoms prefer to disperse in the phosphorus bulk. As Li concentration increases, the difference in the binding energy for different Li distributions becomes smaller and vanishes at around x=0.1. Moreover, the absolute values of the binding energy decrease quickly with increasing Li content, which is similar to the case of Li adsorption on phosphorene surface as illustrated in Fig. 4e. The average voltage for bulk phosphorus is predicted to be 1.7 V. This value is slightly larger than but still qualitatively consistent with the experimental measurement, which is around 0.9-
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1.2V for black phosphorus20, 30. It is interesting to find that the average voltage is 2.9 V (0 ≤ x ≤ 0.25) for monolayer phosphorene, which is obviously higher than that of bulk black phosphorus within the same Li content. Thus the phosphorene-based Li-battery is expected to provide a much higher charging voltage. 46-48
3.5 Electronic property of phosphorene intercalated with Li Consider the fact that Li-batteries have been used to power an increasing diverse range of applications, such as low-current cells used for portable electronics and memory backup and also high-current cells used in military applications, it is essential to understand the electronic properties of electrode materials with resepct to their battery performance. Different from graphene, monolayer phosphorene has a low electronic conductivity because of its semiconducting characteristic with finite bandgap as shown in Fig. 7a.32, 33, 55 Hence, it is essential to examine the electronic properties of phosphorene with Li intercalation. The electronic band structure of phosphorene with Li adsorption at Li0.02P is shown in Fig. 7b. From Bader charge analysis56, the 2s1 electron of Li is completely transferred to phosphorene, which effectively shifts the Fermi energy level into the original conduction band. Hence the complex system has changed from “semiconducting” to “metallic” with considerable electronic states at the Fermi energy level. For the case of lowest Li concentration, Li0.02P, there is one band crossing the Fermi level. The electron distribution correlated to this band is illustrated in Fig. 7c, which is spreading only along the armchair direction and forming the electron conducting channel. However, for larger Li concentration like Li0.042P, the conducting electron spreads in the whole phosphorene layer, displaying less direction dependence as shown in Fig. 7d.
4. Conclusion
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To conclude, by performing density functional theories calculations, we have analysed the Li adsorption and diffusion in phosphorene monolayer and also inside the bulk. Our studies show that Li atom is able to form stable adsorption with phosphorus atoms with a binding energy around -1.9 eV. Upon adsorption, Li denotes its 2s1 electron to phosphorus and exists in the cationic state. The adsorbed complex becomes metallic, which is essential for use as an electrode. Modulated by its puckered structure, the diffusion of Li on phosphorene is highly anisotropic, with diffusion along the zigzag direction being highly energetically favourable, while diffusion along the armchair direction is almost prohibited. Specifically, the energy barrier along the zigzag direction is only 0.08 eV for Li in monolayer phosphorene, much lower than that in two other Li-Battery anode candidates, graphene and MoS2. Furthermore, the average voltage of the Li intercalation is estimated to be 2.9 V, suitable for high charging voltage applications. Based on our present findings, monolayer phosphorene is expected to be used in novel electronic device and Li-Battery with a high charging voltage and high rate capability.
Acknowledgement This work was supported by the A*STAR Computational Resource Centre through the use of its high performance computing facilities, the National Natural Science Foundation of China (grant no. 11304214) and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).
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Figure 1. (a) Schematic of Li surface loading (adsorption process), diffusion along armchair and zigzag directions on phosphorene surface; (b) total potential energy of Li on phosphorene surface with respect to Li-phosphorene distance and (c) charge density difference between Li and phosphorene, indicating electron transfer from Li to phosphorene.
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Figure 2. (a) Energy profiles of Li diffusion along armchair and zigzag directions on phosphorene surface (S1, S2 and S3 denote the saddle points; B1, B2 and B3 denote the binding sites); (b), (c) top view and side view of Li diffusion pathway along the armchair direction; (d), (e) top view and side view of Li diffusion pathway along the zigzag direction.
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Figure 3. (a) Energy profiles of Li diffusion along armchair and zigzag directions in black phosphorus (S1 and S2 denote the saddle points; B1, B2 and B3 denote the binding sites); (b), (c) Top view and side view of Li diffusion pathway along the armchair direction, S1 indicates the Li position at the saddle point; (d), (e) Top view and side view of Li diffusion pathway along the zigzag direction, S2 indicates the Li position at the saddle point.
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Figure 4. (a-d) Configutations of schematics of LixP with Li binded on one side of phosphorene; and (e) binding energies with increasing Li content.
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Figure 5. Calculated voltage profile with respect to Li content from 0 to 0.25.
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Figure 6. (a-c) Binding positions of two Li atoms distributed in a 4 × 3 black phosphorus supercell: First Li is always on position 0 on top of layer 1, second Li can be on positions 1-4 on top of layer 2. In detail, position 1 is on the top of position 0, position 2 is obtained by shifting half lattice vector length from position 1 along b direction, position 3 is obtained by shifting half lattice vector length along a direction, and position 4 is obtained by shifting half lattice vector length along both the a and b directions. (d) binding energies with increasing Li content.
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Figure 7. Electronic band structures of (a) pristine phosphorene and (b) phosphorene with Li intercalation. The blue-colored dash lines indicate the Fermi energy level. Electron density distributions of the bands crossing the Fermi energy level of system (c) Li0.02P and (d) Li0.042P (isosurface = 0.0007|e|/bohr3).
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