Metallic P₃C monolayer as anode for sodium-ion batteries

Abstract

Sodium-ion batteries (SIBs) have become one of the most promising energy storage devices due to the high abundance and safety of sodium. On the other hand, most of the well-developed technologies in lithium-ion batteries (LIBs) can be migrated to SIBs. However, unfortunately, the known anode materials are not suitable in SIBs as a result of the larger atomic radius of sodium compared with lithium. Phosphorus demonstrates an unprecedented high theoretical capacity in SIBs, but its inherent low electrical conductivity and huge volume expansion upon sodiation greatly restrict the cycle stability. Two-dimensional materials as electrodes have shown unique advantages in contrast to their bulk counterparts. In this work, we identify a hitherto unknown P₃C monolayer with a puckered honeycomb structure through first-principles swarm-intelligence structure calculations. More intriguingly, the predicted theoretical capacity of P₃C as an anode for SIBs is up to 1022 mA g h⁻¹, corresponding to a stoichiometry of P₃CNa₄. Metallic P₃C and P₃CNa₄ can provide good electrical conductivity during the battery cycle. The acceptable barrier energy and lower open-circuit voltage ensure good rate capacity and safety in practical applications. Its outstanding performance is attributed to the unique arrangement of two kinds of hexagon rings (i.e. P₆ and P₄C₂), producing high cohesive energy and thermodynamic stability. These desirable properties render P₃C monolayers as a promising two-dimensional material for application in SIBs.

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Introduction

Sodium (Na) is more abundant and evenly distributed in the earth than lithium. Moreover, the mature technologies of lithium-ion batteries (LIBs) can be migrated to sodium-ion batteries (SIBs) owing to the similar chemical properties of lithium (Li) and Na.¹ Therefore, SIBs are deemed to be promising energy storage devices and attractive alternatives to LIBs, so alleviating reliance on increasingly depleted lithium sources.^2,3 A very tricky scientific issue in SIBs is the performance of anode materials, because the well-developed ones in LIBs are unsuitable for SIBs as a result of the larger atomic radius of Na compared with Li.^4–6 For example, commercial graphite in LIBs hardly accommodates Na ions. To solve this problem, various kinds of materials (e.g. carbonaceous compounds,^7,8 phosphorus (P) allotropes,^9–12 phosphides,^13–15 sulfides^16,17 and metal alloys^18–24) have been tried in SIBs. Unfortunately, their performance is still far from satisfactory. Therefore, design and preparation of anode materials with desirable properties is indispensable to develop high-performance SIBs.²⁵ To accelerate the development of SIBs, many theoretical efforts have been made through structure screening,²⁶ prediction,^27,28 and structural modification^29,30 to search for ideal anode materials. Moreover, theoretical calculations play an important role in understanding the charge/discharge mechanisms and electronic properties of electrode materials.^31,32

Among various anode material candidates for SIBs, black P has received much attention due to its remarkable large theoretical capacity (i.e. 2596 mA g h⁻¹) and high stability.³³ However, its large volume expansion (∼400%) upon sodiation leads to rapid capacity fading thus impeding battery performance. On the other hand, the low electrical conductivity of black P decreases the reversibility of the cyclic and coulombic efficiency of the battery.³⁴ After extensive efforts, P/C composite materials have been found not only to have high mechanical stability, but also to improve electrochemical performance with respect to black P.^35–38 This is attributed to formation of P–C bonds and the good electrical conductivity of C.³⁰

Two-dimensional (2D) materials as anodes exhibit unique advantages, in contrast to their bulk counterparts, such as large surface–volume ratio, broad electrochemical window, fascinating chemical activities, and excellent mechanical strength.^39–42 Some 2D materials (e.g. graphene,⁴³ transition metal oxides,⁴⁴ and transition metal dichalcogenides⁴⁵) have exhibited excellent performance in LIBs. Phosphorene, stripped from black P, demonstrates intriguing electron properties.⁴⁶ Phosphorene as anode in SIBs shows acceptable theoretical capacity, however, its inherent non-metallic nature affects electrochemical performance.^12,47 Once again, phosphorene–graphene hybrid material shows high performance, in which graphene serves as a mechanical backbone and an electrical highway.^38,48 By all appearances, the combination P and C is an effective way to enhance performance of the anode. A natural and immediate thought is therefore to examine whether P and C could form stable two-dimensional compounds with high performance in SIBs.

Considering the high capacity of P as anode, we mainly focus on P-rich P–C stoichiometric monolayers. In this work, an extensive structural search was carried out with various stoichiometries (P_xC_y, x = 1–8 and y = 1) through first-principles swarm structural search calculations. As expected, a stable and metallic P₃C monolayer with a buckled hexagonal structure was identified. More importantly, the P₃C monolayer shows high adsorption capacity for sodium (i.e. P₃CNa₄), corresponding to a theoretical capacity of 1022 mA g h⁻¹. The intrinsic metallicity of P₃C and P₃CNa₄ ensures a good rate performance. The Na diffusion barrier of 0.19 eV in the P₃C monolayer is comparable to that of the well-known Ti₂C³⁹ and Sb.⁴⁹ Its high cohesive energy and thermodynamic stability provide good opportunities for experimental synthesis.

Computational methods

A structure search has been carried out by employing a particle swarm optimization algorithm as implemented in the CALYPSO code,⁵⁰ which is a leading structure prediction method in the field. It can efficiently find ground or metastable structures depending on just the given chemical compositions and its validity has been confirmed by the application to both bulk^51–54 and two-dimensional materials.^55–59 The structure optimizations and property calculations were performed by using the density functional theory method⁶⁰ within the generalized gradient approximation of Perdew–Burke–Ernzerhof (GGA-PBE)⁶¹ as implemented in the VASP code.⁶² The ion–electron interaction was described by the projector augmented wave (PAW) technique,⁶³ and van der Waals interactions were taken into account.⁶⁴ To eliminate interactions between adjacent layers, a large vacuum distance of ∼20 Å along the c-axis was used and a plane-wave cutoff energy of 700 eV was employed. Phonon dispersion calculations were based on a supercell approach, as used in the Phonopy code,⁶⁵ in order to determine the dynamical stability of the predicted structure. The thermal stability was analyzed through first-principles molecular dynamics (MD) simulations.⁶⁶ Detailed descriptions of the computational method can be found in the ESI.† The cohesive energy of the P-rich monolayer was calculated by using the following formula:

E_coh = (xE_P + E_C − E_PxC)/(x + 1) (1)

The adsorption energy of the Na atom on the P₃C monolayer can be obtained by:

E_ad = (E_P3C + nE_Na − E_P3CNan)/n (2)

Here, the positive adsorption energy indicates that the P₃C monolayer has the intrinsic ability to adsorb Na ions. The average open-circuit voltage (OCV) is evaluated by the equation expressed as:

where E_P, E_C, E_Na, E_P3C, and E_P3CNan are the total energies of a single P atom, a single C atom, a Na atom in body-centered cubic (bcc) structure, one unit cell of the P₃C monolayer, and the sodiated monolayer, respectively.

Results and discussion

A stable P₃C monolayer with C₂/m symmetry was identified through comprehensive structure search calculations. Its basic building blocks are P₆ and P₄C₂ rings. The alternative arrangement of the two kinds of hexagon rings makes the P₃C monolayer stabilize in a puckered single-layered structure akin to the structural configuration of layer-structured GeP₃,^67,68 InP₃,⁶⁹ and SnP₃ (ref. 70) (see Fig. 1a). In more detail, each atom is three-fold coordinated with the same or other atoms, having P–P and P–C distances of 2.28 Å and 1.78 Å, which are comparable to that in black P (2.22 Å)⁷¹ and almost the same as that in β₀-PC (1.77 Å).⁷² Their covalent bonding characters are evidenced by the presence of localized electrons between two nearest-neighbor atoms, as clearly shown in the plot of electron localization function (ELF, Fig. 1b). On the other hand, the slight torsion of two hexagon rings causes the P₃C monolayer to have a thickness of 1.31 Å, which is much thinner than phosphorene (thickness of 2.10 Å)¹² and GeP₃ (thickness of 2.44 Å).⁷³ Considering these characteristics, P₃C monolayers have a large surface–volume ratio,^74,75 facilitating intercalation of Na, as discussed later.

Fig. 1 (a) Optimized structure of P₃C monolayer with C₂/m symmetry. (b) Electron localization function (ELF) of P₃C monolayer. (c) Decomposed PDOS of P₃C monolayer, projected on four orbitals (s and p_x,y,z) of P and C atom.

The feasibility of experimental synthesis of the predicted two-dimensional materials correlates closely with the amount of cohesive energy.^59,76 The larger the cohesive energy, the easier is experimental synthesis. The resultant cohesive energy of 4.18 eV per atom is significantly higher than that of synthesized phosphorene (3.48 eV per atom)⁷⁷ or GeP₃ (3.34 eV per atom),⁷³ and is comparable to that of the 1T-NiSe₂ monolayer (4.66 eV per atom)⁷⁸ and the 2H–CoTe₂ monolayer (4.48 eV per atom).^79,80 Notably, a layer-structured GeP₃/C nanocomposite has been synthesized showing excellent Li storage performance.⁸¹ Besides, the absence of the imaginary frequency mode in the whole Brillouin zone indicates the dynamical stability of the P₃C monolayer (Fig. S1a and b†). As shown in projected phonon density of states (PHDOS), the appearance of extensive overlapping between P and C vibrations confirms a strong interaction in the P–C bond. To examine the temperature-dependent stability, we performed MD simulations at 1000 K. The framework of the P₃C monolayer maintains its original configuration (Fig. S1c and d†) after simulation. However, the interlayer interaction caused by unique structural characters (i.e. P lone pair electrons, C dangling bond) might hinder synthesis of the P₃C monolayer. This inspired us to probe the feasibility of synthesizing the P₃C monolayer. According to the symmetry of P₃C, five kinds of bilayer stacking patterns can be considered to investigate the exfoliation energy (Fig. S2†). After full structural relaxation, including van der Waals interaction, a stable P₃C bilayer is obtained. The interlayer distance of 4.05 Å (Fig. S2d†) is much larger than for graphite (3.23 Å)⁸² and black phosphorus (3.10 Å).⁸³ Moreover, the exfoliation energy of the P₃C bilayer is 25.2 meV Å⁻², which is smaller than hexagonal BN (28 meV Å⁻²) and slightly larger than graphene (21 meV Å⁻²) and phosphorene (22 meV Å⁻²).⁸⁴ These results suggest that our predicted P₃C has outstanding thermal and dynamical stability and favors experimental synthesis.

To better understand the nature of the chemical bonding and electron properties of the P₃C monolayer, we calculated its electronic band structure (Fig. S3†) and projected density of states (PDOS) (Fig. 1c). As can be seen in Fig. 1c, there is a large overlap of P and C orbitals below the Fermi level, indicating the formation of covalent bonds between P–P and P–C, which is consistent with the structural analysis given above. More intriguingly, the P₃C monolayer is metallic because of several bands across the Fermi level, which is in sharp contrast with the GeP₃ monolayer with semiconducting character,⁷³ having similar atoms arrangement and electronic configuration between P₃C and GeP₃. However, in contrast to C, the large atomic radius of Ge leads to a dihedral angle of 38.64° in the GeP₃ unit, which is much bigger than the 10.67° in the P₃C unit. With replacement of the Ge atoms in the GeP₃ monolayer with C atoms, the GeP₃-structured P₃C monolayer is a semiconductor with a band gap of 0.16 eV (Fig. S4†). In the P₃C monolayer, one C atom with the other three P atoms forms quasi-sp² hybridization, leaving one C 2p_z free electron. Each P atom adopts an sp³ hybridization, in which one of the hybrid orbitals is filled with a lone electron pair (3p_z), and the other three hybrid orbitals form covalent bonds with the neighboring C and P atoms. However, the dihedral angles in P₃C are 106.20° and 88.58°, which is distant from the typical sp³ hybridization of 109.47°. The imperfect sp³ and sp² hybridization of P and C provides delocalized electrons, which might be responsible for the metallic behavior. This point can also be found from the PDOS (e.g. the main contribution of PDOS around the Fermi energy level coming from C 2p_z and P 3p_z orbitals, Fig. 1c). To confirm this, we performed hydrogenation on the P₃C monolayer (Fig. S5†). The added H atoms can immobilize the delocalized electrons donated by C or P.⁸⁵ Both P₃CH and HP₃C are semiconducting (Fig. S5c and d†). A similar phenomenon has been observed in the β₀-PC monolayer.^72,85

The P₃C monolayer is expected to be a potential anode material in SIBs in view of its favorable stability, structural character, and inherent metallicity. For anode materials, spontaneously adsorbing Na atom is one of the necessary conditions. Considering the symmetry of the P₃C monolayer, nine possible adsorption sites were considered (Fig. S6†). After full geometrical relaxations, there are two favorable adsorption sites (A₁ and A₂), localizing at the top of the C atoms (A₁) and the P₆ ring (A₂), as shown in Fig. 2a and b. The resultant adsorption energies at A₁ and A₂ sites are 1.08 eV and 0.90 eV, respectively, indicating that our predicted monolayer can adsorb Na ions. The larger adsorption energy at the A₁ site can be attributed to the delocalized electrons on the C surface providing a suitable habitat for Na ions. As can be seen in the ELF (Fig. S7†), the interaction type between Na and C is ionic with a Na–C distance of 2.49 Å. This is further supported by the Bader charge analysis: each Na atom transfers 0.84 electrons to the C atom.

Fig. 2 (a) Na adsorbs at top of the lower C atom, named A₁. (b) Na sits at the center of a P₆ ring, as A₂. (c) The considered migration paths of Na diffusion on the P₃C monolayer. (d) The corresponding diffusion energy barrier profiles of Path I and Path II.

The Na ion diffusion energy barrier has a great effect on the charging and circuit rate capacity of SIBs. Based on the above results, there are two different diffusion paths for Na ion (I and II, Fig. 2c) between the two nearest-neighbor low-energy adsorption sites. The calculated diffusion energy barriers are shown in Fig. 2d. Path I (i.e. A₁ → A₂ → A₁) has the lowest diffusion energy barrier, of 0.19 eV, whereas the diffusion energy barrier of path II, which is directly from an A₁ site to another nearest A₁ site, is up to 0.46 eV. Based on the above analysis, the P₆ ring plays a key role in accelerating Na-ion migration. Notably, the diffusion energy barrier is much lower than that of traditional MoS₂ (0.28 eV)⁸⁶ and comparable with that of Ti₂C (0.18 eV)³⁹ and Sb (0.21 eV).⁴⁹ To clarify the migration paths I and II, the movement trails of adsorbed Na ion crossing the energy barriers are shown in Fig. S8.† Notably, the diffusion length of 7.30 Å in Path I is similar to 7.09 Å in Path II.

To determine the specific capacity of the P₃C monolayer, we explored concentration-dependent Na ion adsorption behavior on the P₃C monolayer. Four different Na concentrations (P₃CNa_n, n = 1–4) have been used to simulate the adsorption process. All the most stable configurations of the four considered stoichiometries are shown in Fig. 3. The resultant adsorption energies (i.e. 0.97, 0.53, 0.48, and 0.35 eV for P₃CNa₁, P₃CNa₂, P₃CNa₃, and P₃CNa₄) indicate that the P₃C monolayer favorably holds Na ions in these Na ion concentrations. Determining the relative stabilities of P₃CNa_n is important to understand which P₃CNa_n has a more favored formation in the sodiation process. The calculated formation energies of each P₃CNa_n with respect to the P₃C monolayer and body-centered cubic Na solid can be used to build the convex hull (Fig. S9†). In general, a structure whose formation energy lies on the convex hull (i.e. the solid line) is deemed stable with respect to decomposition into other compounds or elemental solids, whereas a structure whose formation energy sits above the convex hull is metastable. In our case, P₃CNa and P₃CNa₃ sit on the solid line, but P₃CNa₄ lies slightly above the solid line. This means that P₃CNa₄ has a greater possibility of forming during the dynamic charge/discharge processes.^87,88 For P₃CNa₄, the P₃C monolayer spontaneously adsorbs two-layer Na atoms (Fig. 3d) on its sides, forming P₃CNa₄. This can be understood by the unique distribution of the dispersive electron cloud (Fig. 4a and b) acting as anion,^89,90 which plays a dominant role in stabilizing the second-layer Na ions. In addition, electron clouds distributed around Na ions can effectively alleviate repulsive interactions between Na ions.⁹¹

Fig. 3 The top and side views of optimized adsorption configuration for the four different Na concentrations (i.e. (a) P₃CNa, (b) P₃CNa₂, (c) P₃CNa₃ and (d) P₃CNa₄).

Fig. 4 ELF map of P₃C with (a) one-layer and (b) two-layer Na atoms.

Finally, we studied the anode performance of the P₃C monolayer. Besides the good thermodynamic stability mentioned above, P₃C in P₃CNa_n (n = 1–4) only shows slight structural distortion. As we expected, the stoichiometry P₃CNa₄ corresponds to a theoretical capacity of 1022 mA g h⁻¹, which is much higher than that of known anode materials (e.g. graphite⁹² is 284 mA g h⁻¹, TiO₂ (ref. 93) is 193 mA g h⁻¹, and MoS₂ (ref. 94) is 350 mA g h⁻¹). Even if the final product of sodiation could not reach P₃CNa₄, the stable P₃CNa₃ stoichiometry can also achieve a theoretical capacity up to 766.5 mA g h⁻¹. The OCV values for different Na concentrations (e.g. 0.97, 0.53, 0.48, and 0.35 V) are in the range of 0–1.0 V, which can efficiently prevent dendrite formation of alkali metals during the discharge/charge process.^95,96 The inherent metallicity of the P₃C monolayer is beneficial for rate capacity. More intriguingly, except for P₃CNa, the other three adsorption stoichiometries (i.e. P₃CNa₂, P₃CNa₃, and P₃CNa₄) are still metallic (Fig. S10†). P₃CNa shows a band gap of 0.77 eV, which is much smaller than the reported sodiation products of black P (e.g. Na₃P₁₁ is ∼1.81 eV, Na₃P₇ is ∼1.94 eV, and Na₃P is ∼1.67 eV).³³

Under experimental conditions, anode materials could consist of multiple monolayers. This inspired us to explore the intercalation of Na within layers and the resultant volume expansion, which closely correlates with practical applications. Here, we mainly focus on the most stable P₃C bilayer, as discussed above. As shown in Fig. S11,† the P₃C bilayer can adsorb two-layer Na atoms within the layer with an adsorption energy of 0.63 eV, which is larger than 0.48 eV for P₃CNa₃ and 0.35 eV for P₃CNa₄ with Na atoms on both sides of P₃C monolayer. The interlayer distance of sodiation for the P₃C bilayer is 9.51 Å, corresponding to a volume expansion of ∼135% with respect to the P₃C bilayer.^33,97 This is much smaller than the volume expansion of black phosphorus (∼400%).³³ Finally, we investigated whether the sodiation P₃C bilayer can be restored to its original configuration. After removing all the adsorbed Na atoms, the relaxed P₃C bilayer recovered its initial structure.

Conclusion

In this work, a novel P₃C monolayer with a puckered honeycomb structure has been found through swarm-intelligence structural search calculations, with large cohesive energy and good thermodynamic stability. The P₃C monolayer can spontaneously adsorb Na ions with an unexpected stoichiometry of P₃CNa₄, leading to a remarkably large theoretical capacity of 1022 mA g h⁻¹. Its Na ion diffusion barrier is as low as 0.19 eV, ensuring a rapid charge/discharge rate capacity for SIBs. The inherent metallicity of the P₃C monolayer provides good electron conductivity. Its structural integrity can be well maintained in the sodiation process. By all appearances, our predicted P₃C monolayer is a promising anode material for SIBs, and awaits experimental confirmation.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This research was supported by the Natural Science Foundation of China under No. 21573037, 21873017, 11704062, and 51732003, the Postdoctoral Science Foundation of China under grant 2013M541283, and the Natural Science Foundation of Jilin Province (20150101042JC), and the Fundamental Research Funds for the Central Universities (2412017QD006).

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Footnotes

† Electronic supplementary information (ESI) available: Detailed description of the computational method and structural prediction, main structural parameters, relative stability, electronic energy band structure, PDOS, average voltages, phonon dispersion curves, and temperature-dependent molecular dynamical simulations. See DOI: 10.1039/c8ta09155b

‡ These authors contributed equally.

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