Exploring the potential of MB₄ (M = Cr, Mo, and W) MBenes as high-capacity anode materials for Ca-ion batteries: a DFT approach

Abstract

Two-dimensional MBene monolayers can be used in rechargeable metal-ion batteries because of their layered structure, abundant accommodating sites and high specific surface area. Owing to the abundant resources and cost effectiveness of calcium, calcium ion batteries (CIBs) are a suitable alternative to Li-ion batteries (LIBs). In this study, the performance of MB₄ (M = Cr, Mo, and W) monolayer MBenes as an anode material for calcium ion batteries has been predicted via a density functional theory approach. We found that these monolayers have a thermally, mechanically, and dynamically stable structure. Furthermore, the lightweight properties and energetically favorable adsorption of 6 layers of Ca atoms endow CrB₄, MoB₄ and WB₄ with high storage capacities of 3377 mA h g⁻¹, 2311 mA h g⁻¹ and 1416 mA h g⁻¹, as well as comparatively low average open circuit voltage of 0.45 V, 0.47 V and 0.35 V, respectively. This reveals their notable superiority over most 2D anode materials. Likewise, the faster mobility of Ca ions in the MB₄ monolayer was proved by low activation barriers values of 0.67 eV, 0.72 eV and 0.79 eV for CrB₄, MoB₄ and WB₄, respectively. Additionally, the metallic nature of the materials remained well maintained after the adsorption of full concentrations of Ca ions. These properties signify that monolayers CrB₄, MoB₄ and WB₄ are promising anode materials for CIBs with commendable rate capacities.

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1 Introduction

In recent decades, Li-ion batteries (LIBs) have appeared as the primary means of converting and storing electrical energy. High energy-density and less expensive energy-storage devices are necessary, nevertheless, because of the quick development of commercial electric vehicles (EVs) and large scale grid energy storage.^1,2 However, another obstacle to the quick development of LIBs is the inadequate lithium reserves in nature, which raises the price of LIBs.^3,4 Therefore, it becomes crucial from an intellectual and scientific standpoint to develop next-generation batteries that use ions other than Li ions as a charge carrier called non-Li metal ions.⁵ Non-Li metal-ion batteries (NLMIBs) have thus far been the subject of much research and have gained attention from the academic community. Examples of NLMIBs include Na-, K-, Mg-, Ca-, and Al-ion batteries. Because of their high valence state and light weight, some of these NLMIBs may have greater theoretical capacities since they employ multivalent metal-ions such as Mg²⁺, Ca²⁺, and Al³⁺.^6–10 More significantly, in comparison to Li, all these metal ions are easily available in the earth's crust. It is imperative to develop and seek out high-efficiency electrode materials to expedite the advancement of NLMIBs, although bulk materials have been examined and reported for the use of high capacity electrode materials for NLMIBs, such as monolayered transition-metal oxides¹¹ and polyanion compounds.¹²

The large ionic radius of non-Li metal ions and augmented coulombic attractions towards multivalent ions impede their rate performance.¹³ Because they are inexpensive, non-toxic, and readily available, calcium-ion batteries (CIBs) are seen as appropriate substitutes to lithium-ion batteries. CIBs are starting to emerge as the rechargeable battery technology of the future.¹⁴ For next-generation electrochemical applications, CIBs may be a better choice than LIBs due to the following advantages: (a) the divalent character, which promotes stronger bonding and storage of one electron for lithium and two for each Ca-atom, which results in an increased theoretical volume and specific capacity; (b) natural abundance;¹⁵ (c) calcium may be electrodeposited smoothly without any dendritic development problems that are cause in metallic lithium; (d) because of its lower radius, diffusion is more rapid than that of lithium ions.¹⁶ The metal ion batteries' performance is also significantly impacted by the selection of materials used for the anode of the batteries. Li-ion batteries predominantly employ graphite as their negative electrode material, characterized by the modest theoretical capacity of 372 mA h g⁻¹, which prevents it from being developed further for energy storage purposes.^17,18 Therefore, to remedy this condition, new anode materials are desperately needed. In this context, two-dimensional (2D) materials offer greater space for these massive metal ions and a smooth surface structure that facilitates the multivalent ions' rapid diffusion, removing the constraint present in bulk materials.^19,20

Two-dimensional (2D) materials possess a large surface area, exceptionally fast electron mobility, and superior mechanical qualities^21,22 that are particularly interesting as anode materials for LIBs and NIBs.²³ A 2D electrode material for LIBs that has been demonstrated thus far is graphene.^24,25 Novel 2D materials have since been researched as potential anode materials for metal ion batteries. These materials include silicene,²⁶ phosphorene,^27,28 borophene,^29,30 boron phosphide,³¹ Mo₂C,³² and 2D transition metal carbides or nitrides, known as MXenes.^33,34 The selective etching of A atoms from MAX phases using hydrofluoric acid (HF) at room temperature can be used to synthesize MXenes.^33,34 Guo et al.³⁵ looked into novel 2D transition metal borides (TMBs) for LIBs. It has been determined that in comparison to the most popular graphite anode (372 mA h g⁻¹ and 0.3–0.5 eV), many 2D materials offer a much higher energy storage capacity (theoretical capacity of >400 mA h g⁻¹) and fast ion diffusion dynamics (diffusion energy barrier height of <0.1 eV) for Li ion batteries. MBenes are a broad class of two-dimensional materials that are synthesized similarly to MXenes and are typically formed from transition metal borides.^36–39 A valence electron deficiency state in the related crystal structures is promoted by the boron-rich chemical environment of MBenes, which results in strong contacts between the metal ions and the electrode materials. Through the use of first principles calculations, it was determined that Cr₂B₂, Fe₂B₂, Mo₂B₂, and W₂B₂ were the four types of MBenes that were anticipated to be formed from Cr₂AlB₂, Fe₂AlB₂, MoAlB, and WAlB through selective etching techniques. The synthesis of 2D Mo₂B₂ and Cr₂B₂ was successfully done by these techniques. The applications and extensive research on MBenes has been made possible by the previous findings.^40,41

A multi-layer adsorption mechanism for metal ions is expected to be supported by the improved chemical interactions between the MBenes and the electron donors (alkaline or alkaline earth metal), leading to an ultra-high ion storage capacity (>1000 mA h g⁻¹). Indeed, the adsorption mechanism of alkaline (earth) metal ions on MBenes has been confirmed by several earlier density functional theory-based theoretical computations. Jia and coworkers³⁹ anticipated the electrochemical characteristics of several type MBenes, such as V₂B₂, Cr₂B₂, Mn₂B₂, Ti₂B₂, Zr₂B₂, and Nb₂B₂, for alkaline metal ion batteries. The extraordinary qualities of these materials like outstanding electronic conductivity, large surface area, different types of crystal structures make them good for energy storage and conversion applications.^42–46 To investigate the suitability of the 2D boron sheet borophene as an electrode material for MIBs, various research has been conducted on the Ag (111) substrate. The storage capacities of Li, Na, K, Mg and Ca ions and their adsorption behavior are studied on the different monolayers of boron-based materials, and it was found that the boron-based materials can be the best choice as anode materials in the metal ion batteries. Yang et al. studied CrB, MnB, FeB, SrB₈ and TiB₄ for the Li-, Na-, K-,Mg- and Ca-ion batteries.^47,48 Research has shown that monolayer TiB has storage capabilities of 408.421 mA h g⁻¹ for Li ions and 328.162 mA h g⁻¹ for Na ions, respectively. These results underline the material's potential for use in energy storage applications.⁴⁹ Monolayer Ti₂N has demonstrated notable capacities, with 484 mA h g⁻¹ for Li ions and 242 mA h g⁻¹ for K ions recorded.⁵⁰ The capacity of 439 mA h g⁻¹ for Li ions, 348 mA h g⁻¹ for Na ions, and 141 mA h g⁻¹ for K ions are demonstrated by monolayer Ti₂C.⁵¹ The capacity of monolayer TiB₄ for Li ions is 510.534 mA h g⁻¹, for Na ions is 390.999 mA h g⁻¹, and for K ions is 316.59 mA h g⁻¹, which are encouraging.⁵² For Mg-ion on Sc₂B, V₂B and Ti₂B, the M₂B phases exhibit ultra-high specific capacities of 3192.813 mA h g⁻¹, 2853.953 mA h g⁻¹ and 3018.414 mA h g⁻¹, respectively.⁵³ TiB₄ has a Ca storage capacity of 1176 mA h g⁻¹, and SrB₈ has a Ca storage capacity of 616 mA h g⁻¹.⁴⁷

Inspired by the previous investigations, we selected the first three elements of group VI and designed the MB₄(Cr, Mo, W) using the computational structure prediction method in the framework of density functional theory. To determine the possibility of monolayer MBenes (CrB₄, MoB₄, and WB₄) with dynamic stability and an electronic configuration as anode materials, we investigated these materials. It was also thoroughly studied how the monolayer MBenes behaved in terms of adsorption, diffusion barriers, maximum theoretical capacity, and average open-circuit voltage. According to the test findings, these monolayer MBenes show promise as cathode/anode materials.

2 Computational detail

In this study, advanced computational tools were used to explain the behavior of the materials for CIBs under different conditions. The well-known Vienna ab initio simulation package (VASP) was employed for their adaptability and precision in the simulating the complex system at the atomic scale and was conducted by the used of various density functional theory (DFT) frameworks.^54,55 To understand the material structure stability and dynamic behavior, the study effectively recorded the complex interactions of the electrons and ions within the materials using the plane-wave approach with cutoff energy of 550 eV. These values were determined through a convergence test of cutoffs based on the total energy, as shown in Fig. S1.† The exchange–correlation energy is represented by the Perdew, Burke, and Ernzerhof (PBE) functional,^56,57 12 × 12 × 1 k-points were used for geometry optimization and 5 × 5 × 1 Monkhorst–Pack k-points was used for the 3 × 3 × 1 supercell of MB₄, assuring a thorough investigation of the phase space of the materials. A vacuum space of 18 Å was introduced for both CrB₄ and MoB₄, while it was 20 Å for WB₄ to investigate the interactions between the neighboring layers. The convergence test was also employed to determine the K-points and vacuum space, as shown in Fig. S2–S4.† GGA-PBE was utilized for electronic structure calculations, followed by the HSE06 hybrid density functional method to delve deeper into the material's electronic properties and analyze its band structure.^58,59 The DFT-D3 approach was used for the consideration of long-range van der Waals interactions.^60,61 Density functional perturbation theory (DFPT) was used to investigate the dynamical stability of the studied materials, and PHONOPY code was used to investigate the phonon characteristics.⁶² The convergence criteria were thoroughly specified at −0.02 eV Å⁻¹ established at Hellmann–Feynman force and a total energy value of 10⁻⁸ eV, which promised reliability and precision of the phonon computations. Charge transfer from the Ca-ion to the CrB₄, MoB₄ and WB₄ monolayer was performed by the Bader charge analysis that provides the charge pathway through the materials. Moreover, the structure stabilities and adsorption of Ca-ion layers on the studied materials for anode ab initio molecular dynamic simulations (AIMD) was carried out at 300 K (room temperature) over the 5 ps time scale, which provides an insight into behaviors of the materials' structure at room temperature.^60,61 VASPKIT code was used for the analysis and interpretation of the various simulation results of pre and post processing of a vast amount of data.⁶³ Furthermore, the dynamical and structural characteristics of the studied materials were investigated under the mechanical parameters, and the phonon frequency was discovered by the Hellman and Feynman theorem with the direct supercell approach, which provides important information about the vibrational properties of the studied materials.⁶⁴ Mechanical parameters like Poisson's ratio and Young's modulus were investigated using the Voigt–Reuss–Hill approximation, and the values of elastic constants were examined using the stress-tensor-created small strain, which provides resilience and mechanical robustness to the materials.⁶⁵ Finally, the charging and discharging processes were investigated using the simulation of surface barriers and minimum energy paths (MEPs) of Ca migration in the MB₄ monolayer with the climbing nudged elastic band (CI-NEB) method. This technique approximately justifies Ca-ion batteries' calcium intercalation/deintercalation mechanisms.^66,67

3 Results and discussions

3.1 Structure of the MB₄ monolayer

To check the suitability of the material for the calcium ion batteries, it is important to check the behavior of Ca atoms on that material. This structure of the material is important; Fig. 1(a) shows the general structure of 2D monolayer MB₄ (M = Cr, Mo, and W), and their optimized side view of structures are shown in Fig. 1(b–d), while Fig. S5(a–c)† represents the top view of the optimized structures of CrB₄, MoB₄ and WB₄, respectively. The Cr/Mo/W layer is sandwiched between two layers of B atoms, the unit cell has four B atoms and one Cr/Mo/W atom, and there is an intermediate triangular layer that is composed of the Cr/Mo/W atom between the two hexagonal sheet of B atoms. These monolayers have 1 : 4 ratio of B atoms to the Cr/Mo/W atom. After the geometry optimizations of the 3 × 3 × 1 supercell of MB₄, the lattice constant and thickness (d) for CrB₄ were found to be 8.67 Å and 3.02 Å, 8.87 Å and 3.28 Å for MoB₄, and 8.88 Å and 3.30 Å for WB₄, which are similar to the previous report on these materials.^68–72 Because the W atom has a larger atomic size than those of Cr and Mo, WB₄ has larger lattice parameters than CrB₄ and MoB₄. One unstable boron atom was located next to the carbon atom sheet in the periodic table. In order to accomplish a completely filled π-bond within the honeycomb, one extra electron is needed for each boron atom, resulting in the 2s²2p² configuration.

Fig. 1 (a) Top view the of MB₄ structure with three stable sites (H, T, and B sites). (b–d) Side view and (e–g) phonon dispersion curve of CrB₄, MoB₄ and WB₄.

The structural stability of boron sheet can be obtained by adding atoms of group VI (like Cr, Mo and W), which involve the two boron-sheets, and the B⁻ anion has the same configuration as the B atom in the structure of graphene since each atom has the potential to contribute four electrons, creating the 2s²p² electrical structure. Every B honeycomb is stabilized by the σ-bonds that is formed by sp² hybrid orbitals, while the σ-bonds between B⁻ anions are formed by the pz orbitals. It is stable and resembles graphene because the B atoms form covalent bonds with other B atoms and ionic bonds with the remaining atoms (Cr/Mo/W). Inside these monolayers, the movement of the high-charge impact is influenced by strong van der Waals (vdW) forces between the two boron sheets, which results in the development of a double Dirac cone. Two Dirac cones appear in the energy window shown in Fig. S6(a–c),† close to the Fermi level.^68–70 Two symmetry cones are visible in the electronic structure: cone I is situated at K, which is above the Fermi level, and cone II is located at the Γ to the K site just below the Fermi level, which shows the metallic behavior of MB₄. In agreement with earlier research, both cones have the Fermi velocities of 5.31 × 105 ms⁻¹, or about half that of graphene.^73–75 The energy band structures of 2D monolayer CrB₄, MoB₄, and WB₄ exhibit distinct energy bands through the Fermi level. When employing the HSE06 method for electronic structure calculations, the investigated material retained its metallic character. Despite the increased accuracy provided by the HSE06 functional, the system's electronic configuration did not exhibit a bandgap, indicating its continued metallic behavior, as shown in Fig. S7(a–c).† This indicates that the MB₄ materials are very suitable for use as electrode materials in Ca-ion batteries because of their metallic conductivity.

Material stability was evaluated when we examined their dynamic stability with an emphasis on the dynamic stability of MB₄. The phonon dispersion curve and projected vibrational density of states (PVDOS) for the monolayers MoB₄, CrB₄, and WB₄ are presented in Fig. 1(e–g), respectively. Positive frequencies are indicative of favorable dynamic stability in all the three materials. We also performed the phonon calculations to check the further dynamical stabilities of both materials under the strain of +2.5% and −2.5% and found no imaginary frequencies, as shown in Fig. S8(a–c) and S9(a–c).† The mechanical stability of the materials used to produce high-capacity anodes must be considered. Batteries must have strong mechanical properties to withstand volume growth caused by charge–discharge cycles because they do not collapse under extreme pressure or stress like other 2D electrode materials do.^76,77 We calculated the in-plane stiffness constants to assess the mechanical stability of anode materials. For a two-dimensional case of material under stress, the Voigt notations 1 − xx, 2 − yy, and 6 − xy,⁷⁸ the total PE U(ε) can be written as follows.⁷⁹

In eqn (1), C₁₁, C₁₂, C₂₂, and C₆₆ are the dimensional elastic-tensor and elastic constants, where C₁₁ represents the materials stiffness when the applied strain is along the x-axis and C₁₂ represents the stiffness when the applied strain is along the y-axis. The capability of the MB₄ material to endure biaxial strain is represented by C₂₂ and the resistance to distortion cause because of the share strain is represented by C₆₆, while ε_xx and ε_yy represent the uniaxial strain along the x- and y-axis, respectively. A methodology similar to that of Barik and Pal was employed, subjecting the material to stresses ranging from −2.5% to +2.5% with a tiny interval of 0.5%.^80,81 A 2nd ordered polynomial was fitted to the uniaxial deformation along x- and the y-axes in order to acquire the strain-energy facts arising from the values of C₁₁ and C₂₂. Similarly, as shown in Fig. S10(a–c),† biaxial planar distortion along the xy-plane yielded the C₁₂ value, where C11 and C₂₂ are equal in the hexagonal system, and an additional relation holds.

Elastic constants values allow for the direct determination of in-plane Poisson's ratio (ϑ) and Young's modulus (Y),⁸² and we can calculate the values with these formula with elastic constant, i.e., Poisson's ratio and Young's modulus A material's response to mechanical deformation is known as elastic instability, and it is correlated with its elastic constants. When many elastic constants exhibit −ve response, it suggests a potential transition of phase or instability of the structure and shows that the crystal structure is no more stable to insignificant deformation; thus, this instability develops. The calculated values of the elastic constant of the materials are shown in Table 1; all these elastic constants followed the Born–Huang^83,84 conditions of stability of the materials, which is C₁₁C₁₂ > 0, C₁₁C₂₂ – C₁₂C₁₂ > 0, C₁₁ > C₁₂, and no value of the elastic constant is negative, which means that all the monolayers are mechanically stable.^80,85 The values of Poisson's ratio and Young's modulus showed a notable degree of flexibility of the materials, and our calculated values are greater than that of some other 2D monolayer materials reported in the literature, i.e., SiP₃,⁸⁶ 2D-SnB⁸⁷ and B₂N₂.⁸⁸ The systematic investigation of the mechanical and physical characteristics yields useful information that advances the manufacture of flexible anode materials for Ca-ion batteries.

Table 1 Calculated elastic constants (N m⁻¹), Young's modulus (N m⁻¹) and Poisson's ratio for CrB₄, MoB₄ and WB₄

Material	C 11	C 12	C 66	Young's modulus (Y)	Poisson's ratio (ϑ)
CrB4	356.26	84.01	136.13	336.45	0.24
MoB4	402.12	58.05	172.04	391.16	0.14
WB4	407.76	61.32	173.22	398.53	0.15

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3.2 Adsorption of Ca on MB₄ monolayer

The adsorption mechanism of Ca on the MB₄ monolayer is governed by the energy surface of the CrB₄, MoB₄ and WB₄ monolayers. Firstly, we calculated the adsorption energy of single Ca-atom on different possible sites on the surface of the MB₄ anode material, and these sites are shown in Fig. 1(a). According to the structure symmetry, we selected the three different adsorption sites, which are labeled as Hollow-site (H-site), Bridge-site (B-site) and Top-site (T-site). Adsorption is only suitable when the material has suitable stable sites; for this purpose, checking the adsorption energy of respective sites is very important for Ca-atom adsorption on the surface of the MB₄ monolayer. For this, we computed the adsorption energy of each site and compared it using the following equation for the adsorption of a single Ca atom.⁸⁹

E_ads = (E_Ca-MB4 − E_MB4 − E_Ca) (2)

In the above equation, the total energy of the MB₄ surface with one Ca atom adsorbed is represented by E_Ca-MB4, and E_MB4 represents the total energy of pure MB₄, while E_Ca denotes the total energy of a single Ca-atom. The adsorption energies of all these three sites are tabulated in Table 2 and graphically represented in Fig. 2(a), which represents that all values of adsorption energies are negative, which is favorable of the adsorption of Ca atom on the MB₄ surface and shows exothermic adsorption, which is the most common form of the metallic cluster. Metallic clusters in calcium-ion batteries improve ion adsorption, diffusion, stability, and conductivity, thereby enhancing the battery performance. The calculated adsorption energies values are −3.94 eV, 3.18 eV and −2.74 eV for the Hollow site; −3.93 eV, −3.27 eV and −2.69 eV for the Bridge site; and −3.20 eV, −2.33 eV and −1.89 eV for the Top site of CrB₄, MoB₄ and WB₄, respectively. It can be seen that the adsorption energies of the Hollow site are more negative as compared to the T- and B-site for all three materials, which indicates that the H-site is the most stable site and is favorable for the further adsorption of Ca atom.

Table 2 Calculated adsorption energy, Bader charge and structural parameters for Ca atoms on both sides of CrB₄, MoB₄ and WB₄

Parameters	Adsorption energy (eV)			Bader charge (e)
	Top	Bridge	Hollow	Top	Bridge	Hollow
Ca0.11CrB4	−3.20	−3.93	−3.94	1.39	1.38	1.40
Ca0.11MoB4	−2.33	−3.17	−3.18	1.31	1.30	1.32
Ca0.11WB4	−1.89	−2.69	−2.74	1.34	1.34	1.35
Height (hs–s) of CrB4	3.02 Å
Height (hs–s) of MoB4	3.28 Å
Height (hs–s) of WB4	3.30 Å
Lattice constants (a, b) of CrB4	8.67 Å
Lattice constants (a, b) of MoB4	8.87 Å
Lattice constants (a, b) of WB4	8.88 Å

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Fig. 2 Adsorption energies (E_ads) of CrB₄, MoB₄ and WB₄. (a) Stable Ca-sites with their respective adsorption energies and (b) average adsorption energies (E_ad) with increasing Ca-adsorbed layers (x = 1, 2, 3, 4, 5, and 6).

After finding the suitable site for adsorption, it is significant to find the interaction behavior of Ca atom on the surface of CrB₄, MoB₄ and WB₄ monolayers. For this reason, we studied the charge exchange between the Ca-ion and these monolayers. Bader charge analysis is a technique that can be used to combine the electrons around an atom with its chemical valence, enabling the analysis of charge transfer between the Ca atom and the MB₄ monolayer before and after the adsorption process, which was used to study whether or not the adsorption process is favorable between Ca and the MB₄ monolayer. For the most stable H-site, Ca atom transferred 1.40e to the monolayer CrB₄, 1.32e to the monolayer MoB₄ and 1.35e to the monolayer WB₄. The charge of the Ca atom transferred from the other adsorption sites to these monolayers with the respective adsorption energies is tabulated in Table 2. The charge transferred values of these sites indicates the strength of strong adsorption, which shows robust chemical interactions between the Ca atom and the material surface, promoting adsorption and increasing the theoretical capacity.^90,91 In a calcium-ion battery, calculating the charge density difference (CDD) when Ca adsorbs on the MB₄ surface aids in the identification of active areas, the prediction of reactivity, and the optimization of the battery performance. For this purpose, we examined the CDD to envisage the chemical reaction of Ca adsorption on CrB₄/MoB₄/WB₄ utilizing the following equation.

Δρ(r) = ρ_Ca-MB4(r) − ρ_MB4(r) − ρ_Ca(r) (3)

In this equation, the charge-density of the MB₄ surface with one Ca atom adsorbed is represented by ρ_Ca-MB4 and ρ_MB4 represents the charge-density of pure MB₄ while ρ_Ca denotes the charge-density of the isolated Ca-atom. As demonstrated in Fig. 3(a–c), while the yellow zone depicts electron accumulation, the green region denotes electron depletion. It shows that a significant amount of charge exchange takes place between the Ca-ion and MB₄ monolayer MBene. There is an extensive charge accumulation between the Ca-atom and MB₄ monolayer MBenes surface, whereas there is charge depletion surrounding the Ca atom. These findings suggest that strong interactions on the surface of MB₄ monolayer MBene may allow Ca ions to be adsorbed steadily.

Fig. 3 Charge density difference for the adsorption of single Ca-ion on the substrate (a) CrB₄, (b) MoB₄, and (c) WB₄.

After finding a suitable adsorption site and the strong interactions with the suitable charge transfer of Ca atom on the MB₄ surface, we examined the possibility of multilayer adsorption in monolayer MB₄ MBenes because the storage capacity of the Ca-ion batteries depends on the number of Ca atoms adsorbed on the surface of MB₄. We considered the top and bottom hollow site of the monolayer's surface for the further adsorption of Ca-atoms. We absorbed the triple layers of Ca atoms on both sides, and we absorbed max 9 Ca-atoms on one layer. In this way, we absorbed a total of 6 layers on both sides including 3 top and 3 bottom surfaces of MB₄, and their adsorption scheme is shown in Fig. S11(a–f),† which indicates the top side and bottom side view of adsorption of Ca-atoms layer on the surface of CrB₄ from layer 1 to layer 6. The second- and third-layer adsorption involved Ca ions occupying the T-site site of the first and second layers at different positions of the T-site. The optimized structure of all Ca-layers adsorption on CrB₄, MoB₄ and WB₄ are shown in Figs. S12–S14(a–f),† respectively, which shows that the structure did not significantly change after adsorption, indicating that Ca ion adsorption by triple layers on the top/bottom surface of MB₄ is feasible. The study reveals that MB₄ MBenes can absorb up to six layers (54 atoms) of Ca ions with no alteration in the system's structure and the maximum adsorption contents of Ca atoms are x = 6, reaching saturation when three layers are adsorbed on each side; we used the following formula to calculate the average adsorption energies (E_ad) of Ca-atom layers.⁹²

E_ad = (E_MB4+xCa − E_MB4 − xE_Ca)/x (4)

In this instance, E_MB4+xCa and E_MB4 represent the total energy of the MB₄ monolayer values with and without Ca-ions adsorption, whereas E_Ca represents the total energy values of Ca in the bulk phase and “x” is the number of Ca atoms absorbed. The calculated average adsorption energies values of Ca layers on the CrB₄, MoB₄ and WB₄ monolayer surface are shown in Table 3 and graphically represented in Fig. 2(b). Negative adsorption energy represents the strong interactions between the Ca ions and the MB₄ monolayer. When the number of the adsorption layers increase, the distance between the Ca layers and MB₄ monolayer increases, which is the reason for the weak interactions of the third layer on both sides, but the adsorption energies remain negative, which is favorable, and we cannot add more layer because the adsorption energies become positive. For the adsorption of a single layer of Ca-atom layers, the interaction between the Ca atoms and the substrate is strong, and when we adsorbed the 2nd and 3rd layers, then the interactions became weak and the upper most layer has weak coulombic interactions with the substrate and the adsorption energy decrease. As the number of layers of Ca atoms increased, the coulombic repulsion between the Ca atoms in the intralayer increased owing to the weak interaction with the substrate and strong coulombic repulsion between Ca atoms. Due to repulsion of Ca atoms in the intralayer, the adsorption energy becomes low but remains negative. Fig. S15† represents the spacing of the interlayer between the adsorbed Ca atoms on the CrB₄, MoB₄ and WB₄ substrate and it can be seen that with the adsorption of multilayers, the distance from the substrate increases and the largest distance of the last layer with the substrate is 7.95 Å, 7.99 Å and 8.32 Å for CrB₄, MoB₄ and WB₄, respectively. The distance of the uppermost layer of the WB₄ layer is larger than CrB₄ and MoB₄ due to the larger atomic size of tungsten atom as compared to Cr and Mo, which shows the strong interactions of Ca atom on the surface of CrB₄ as compared to that of MoB₄ and WB₄. The concentration of Ca ions adsorbed on CrB₄/MoB₄/WB₄ reaches its maximum when the attracting and repulsive electrostatic forces between the Ca ions completely balance each other out. Thus, we cannot consider additional metal layers absorbed onto the substrate.

Table 3 Calculated average adsorption energy of the Ca-adsorbed layer on CrB₄, MoB₄ and WB₄

Material	x 1	x 2	x 3	x 4	x 5	x 6
CrB4	−1.84	−1.36	−0.85	−0.82	−0.36	−0.14
MoB4	−1.66	−1.49	−1.01	−0.93	−0.42	−0.11
WB4	−1.40	−1.11	−0.62	−0.44	−0.39	−0.27

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The formation of a negative electron cloud (NEC) is important for the structural stability of the materials with adsorption and helps to further attract the outer-ions when examining the layer-by-layer adsorption of Ca ions. The valence electron localization function (ELF) is an effective method for analyzing the interactions between Ca ions and the adsorption layer and substrate. In order to illustrate the adsorption mechanism of various Ca ions, we determined the ELF of the (1 0 0) section for the maximum layers of Ca adsorbed on the MB₄ monolayer, as illustrated in Fig. 4(a–c). It should be noted that an electron's full localization is represented by an ELF value of 1, and that the electron-gas-like pair probability is represented by a value of 0.5; the lower value denotes a lower electron density.⁹³ Ionic bond formation was evident in Fig. 4 as electrons were localized between the MB₄ substrate and the first layer Ca adatoms. This demonstrates that the initial layer's steady adsorption of each of these metals is confirmed. Additionally, an integrated NEC layer forms over the Ca layer, guaranteeing the first-layer Ca ions' persistent adsorption on the MB₄ surface and increasing the attraction of additional Ca ions. The localization between the outmost adsorbed Ca atoms steadily rises with the increasing number of adsorption Ca layers. The existence of NEC between Ca layers significantly reduces atom-to-atom repulsion and is essential for enhancing the stability of multilayer adsorption. These findings demonstrate how the covalent and ionic bonds within the MB₄ monolayer coexist, which enhances the monolayer's exceptional structural stability. The Ca ions were almost entirely ionized in each case, suggesting a substantial chemical interaction between these Ca ions and the MB₄ monolayer. By fostering the formation of both covalent and ionic interactions, this robust interaction supports the general stability and adsorption behavior of Ca on the outer MB₄ layer.

Fig. 4 Electron localization functions (ELFs) of the (100) section on (a) Ca₆CrB₄, (b) Ca₆MoB₄, and (c) Ca₆WB₄.

To check the thermodynamic stability of the structures, we calculated the formation energy using the following equation.⁹⁴

E_f = (E_MB4+xCa − E_MB4 − xE_Ca)/x + 1 (5)

In this case, E_MB4+xCa and E_MB4 represent the total energy of the MB₄ monolayer values with and without Ca ions adsorption, whereas E_Ca represents the total energy values of Ca in the bulk phase and “x” is the number of Ca atoms absorbed. The formation energies and the constructed convex hull of Ca-adsorbed MB₄ (M = Cr, Mo, and W) at different concentrations are displayed in Fig. S16(a–c).† For MB₄ structures with Ca adsorbed, we computed six concentrations. Convex hulls form solid lines connecting minimal energies, making thermodynamically stable states. MB₄ monolayer's stable structure and less volume fluctuations benefit its cycle stability and performance as an anode in CIBs for Ca-ion insertion and extraction sequences. Notably, Ca adsorbed-MB₄'s E_f curves (x = 1, 2, 3, 4, 5, and 6) show stability, like the earlier studied two-dimensional materials.^95–97

3.3 Thermal stability

Thermal stability is crucial in calcium-ion batteries to prevent structure deformation, which can compromise the battery's integrity and performance. It prevents excessive expansion or contraction, preserving the structural integrity during the charge and discharge cycles. This prevents mechanical stresses like electrode cracking, particle detachment, or electrolyte leakage, ensuring reliable and long-lasting performance in various operating conditions.

The thermal stability of MB₄ monolayers with Ca ions at various concentrations was investigated using an ab initio molecular dynamics (AIMD) method under the NVT ensemble, and we considered the pristine as well as Ca-ion adsorbed monolayer of MB₄ for a 3 × 3 × 1 supercell. Fig. S17(a–c)† correspond to the energy changes with time steps for the pristine CrB₄, MoB₄, and WB₄ monolayer, respectively, and shows the zero structural deformation of the pure material. From Fig. S18(a–c),† the simulation resulted in the preservation of the two layers of Ca-adsorbed MB₄ monolayer's structural integrity, as evidenced by the simulation's modest oscillations that suggested the monolayer's stability. Nonetheless, the system's energy did not significantly change over the course of the simulation. The structures of Ca₂CrB₄, Ca₂MoB₄, and Ca₂WB₄ did not undergo any notable alterations or deformations during the Ca adsorption process, as demonstrated by our simulated timeline spanning from 1 to 5000 fs. Fig. S19(a–c)† represent the molecular dynamic simulations of full concentrations of Ca ions adsorbed on CrB₄, MoB₄ and WB₄ at 300 K, and we can see that the small structural disorder occurs, which is acceptable according to the literature.^98–102 Additionally, in order to validate the MB₄ (M = Cr, Mo, W) monolayer's thermal stability at high temperatures, we also ran simulations on its maximum Ca configurations at 500 K. The results indicated that the small structures are disordered just like those at 300 K, confirming their stability at high temperatures, as shown in Fig. S20(a–c).† The atomic recombination and chemically breaking of bonds are almost invisible, which is in keeping with the previously reported 2D materials.^98–102 Remarkably, during the adsorption/desorption process, the volume of the Ca ions-adsorbed MB₄ MBenes was less changed than graphite.^103,104 Our findings also showed low energy fluctuations, which supports the thermal and dynamic stability of MB₄ at room temperature.

3.4 Diffusion barrier

To better understand the correlation between the rate capability and cyclability of batteries and the diffusion behavior of Ca ions on the electrode surface, we investigated the diffusion properties of Ca ions on MB₄ (M = Cr, Mo, W) monolayer. The energy barrier for Ca ion diffusion for the MB₄ monolayer was examined using the Cl-NEB method. The energy barrier represents the energy required for the diffusion process to occur. Additionally, we calculated the Ca atoms' MB₄ diffusion coefficient (D) as a function of temperature using the Arrhenius equation as D(T) = a²v_oe^−E_b/k_BT.¹⁰⁵ Here, v_o is the vibrational frequency (10¹³ Hz), E_b is the diffusion barrier, and “a” is the Ca-atom movement distance within the MB₄ monolayer at the adsorption sites. Absolute temperature and Boltzmann constant are represented by the symbols T and k_B, respectively. The diffusion barrier in Ca-ion batteries controls the movement of Ca ions between the MB₄ materials that make up the battery electrode. Diffusion barriers are used in charging and discharging processes to regulate the speed at which ions may move through a substance. Essentially, the lower the energy barrier, the faster the process of ion diffusion. So, by finding the pathway with the lowest diffusion barrier, we can understand the structural symmetry to find the best diffusion path. Considering that Ca tends to be adsorbed on site H1, the possible migration path according to the symmetry of our structure is shown in Fig. 5(a). We considered the two paths as path-1 (H1–H2) starting from the H1-site to the H2-site, and path-2 (H1–T–H2) starting from the H1-site to the H2-site through the T-site.

Fig. 5 (a) Migration path 1 (H1–H2) and path 2 (H1–T–H2) for Ca-ions on the MB₄ monolayer, diffusion energy barriers for Ca-ion diffusion on (b) CrB₄, (c) MoB₄, and (d) WB₄.

To illustrate the process of diffusion and how it progresses between the initial and final site, we chose the three intermediate images, and these images give extra clarification about the diffusion process. Using these intermediate-stage images, we can see the diffusion process from start to end and examine the energy barriers at every turn. The calculated results and schematic diagrams of Ca diffusing on the MB₄ monolayer are summarized in Fig. 5(b–d). The energy barrier profiles show that path-1 has the energy barriers of 0.67 eV, 0.72 eV and 0.79 eV, while path-2 has 0.73 eV, 0.78 eV and 0.84 eV for CrB₄, MoB₄ and WB₄, respectively. In comparison to CrB₄ and MoB₄, the WB₄ surface exhibits high diffusion barriers. This is likely due to the fact that W contains a larger atomic size than Cr and Mo, which could impact Ca-ion interaction with the lattice and raise the diffusion barrier. The results indicate that path-1 has a lower energy barrier than path-2. Our calculated energy barriers are less than the other materials reported for multivalent ion batteries such as α-V₂O₅ (1.63),¹⁰⁶ α-SN (1.58 eV),¹⁰⁷ FePS₃ (1.18),¹⁰⁸ 2D boron (0.79 eV),¹⁰⁹ TiO₂ (1.27 eV),¹¹⁰ MoS₂ (1.12 eV)¹¹¹ and α-SN (1.58 eV).¹⁰⁷ Moreover, these values are greater than some reported 2D anode materials such as borophene (0.62 eV),¹¹² C₂N (0.30),¹¹³ h-BN (0.10 eV),¹¹⁴ bismuthine (0.15 eV),¹¹⁵ and borophene (0.35 eV).¹¹⁶ Moreover, the comparison with other reported 2D materials is tabulated in Table 4 and graphically represented in Fig. S21.† Ca atoms can diffuse over the surface of monolayers CrB₄, MoB₄, and WB₄ with low diffusion potential barriers that allow for quick Ca-ion movement, which boosts the energy efficiency, improves 1.12 cycle stability, and optimizes 1.12 electrochemical performance, preventing undesirable side reactions, guaranteeing the battery's lifespan, and raising the battery's overall efficiency and energy density. All these features make the CrB₄, MoB₄, and WB₄ monolayer excellent anode materials for calcium ion batteries.

Table 4 Comparison of voltage, diffusion barrier, and capacity of MB₄ with those of other materials

Material	Voltage (V)	Diffusion barrier (eV)	Capacity (mA h g^−1)	Ref.
CrB4	0.45	0.67	3377	This work
MoB4	0.47	0.72	2311	This work
WB4	0.35	0.79	1416	This work
SrB8	0.48	0.67	616	47
Borophene	1.59	0.62	964	112
2D boron	1.50	0.79	2125	109
SW-BN	0.89	0.11	1162	117
C2N	0.23	0.30	419	113
FePS3	0.48	1.18	586	108
TiS2	1.4	1.16	—	118
BSi	0.40	1.08	2749	119
C2N	0.23	0.30	419	113
FePS3	0.48	1.18	586	108

---

In practical terms, the adsorption of Ca ions is known to cause considerable volume expansion in electrode materials, hence shortening their service life. Additionally, volume modification is a critical parameter that is examined throughout the monolayer's calcification/decalcification process. For the purpose of volume expansions, the lattice mismatch between the Ca-ions layers and the MB₄ substrate is crucial to the adsorption process, and the smaller the lattice mismatch, the stronger the adsorption of the higher layers.^120,121 When the Ca content increases, we compute the lattice mismatch as shown in Fig. S22(a–c),† which represents the lattice parameters of Ca_xMB₄ with increasing Ca contents. The findings show that the lattice constants change as Ca concentrations rise and at maximal Ca content loading, a very slight lattice mismatch was found. The lattice mismatch values for CrB₄, MoB₄ and WB₄ at x = 6 are 5.94%, 6.16% and 6.31%, respectively. These results validate that there is no cause for concern over lattice mismatch and the adsorption is feasible.

3.5 Electrochemical attributes of Ca-adsorbed MB₄

Ca ions are continuously intercalated into the anode and deintercalated from the cathode in the rocking chair battery during the procedure of charging. The amount of Ca ions that anode materials can store establishes the battery's capacity and it is the number of Ca ions storable per unit mass, which is very important for an efficient electrode material, and the theoretical specific capacity calculation should be based on the structure's maximum Ca intercalation. According to the structure symmetry, we adsorbed Ca atoms on the top/bottom hollow site, 3 layers on the top and three layers on the bottom side with total 54 atoms (9 atoms per layer). The calculated theoretical capacities are 3377 mA h g⁻¹, 2311 mA h g⁻¹ and 1416 mA h g⁻¹ for CrB₄, MoB₄ and WB₄, respectively, for calcium ion batteries. Our calculated values are higher those of commercially available anode materials like SW-BN (1162.66 mA h g⁻¹),¹¹⁷ graphite (284 mA h g⁻¹),⁹¹ MoO₂ (1256 mA h g⁻¹),¹²² Ti₃C₂ (352 mA h g⁻¹),⁹⁰ Mo₂C (560 mA h g⁻¹)¹²³ BC₂N (840 mA h g⁻¹),¹²⁴ and super-B (3718 mA h g⁻¹),¹²⁵ and the comparison with other reported 2D materials is tabulated in Table 4 and graphically represented in Fig. S21.† Within the saturation concentration range, the theoretical storage capacity rises significantly, boasting approximately five times the capacity of graphite, a typical anode material for LIBs.

Subsequently, the average open-circuit voltages associated with the amounts of several Ca cations that are adsorbed were computed. When charging and discharging, the electron potential energy process equals the variation in Gibbs free energy inside the system. The change in the total energy of the Ca atoms before and after adsorption is about equal to this change in the Gibbs free energy when we ignore the small changes in the system's volume and entropy. The open circuit voltage is mostly influenced by the Ca ion distribution in the system, which is defined by the energy differential between two systems with various concentrations of adsorption. To do this, we applied varying concentrations of Ca ions to both sides of the monolayer MB₄ MBenes until they were fully covered, using the Ca_xMB₄ stoichiometry (x = 1, 2, 3, 4, 5, 6). After numerical stabilization in Fig. 6, we used the average voltage curves to calculate the average open-circuit voltages, which shows the decreasing trends of the voltage as the number of Ca layers increased. Our calculated average OCV values are 0.45 V, 0.47 V and 0.35 V for Ca_xCrB₄, Ca_xMoB₄ and Ca_xWB₄, which are lower than that for phosphorene (0.83 V),¹²⁶ TiO₂ (1.5 V)¹²⁷ and borophene (2.63 V).¹¹² The comparison with other reported 2D materials is tabulated in Table 4. It is significant that these average OCV values are within the recommended range of 0–1.0 V for anode materials that are readily available for use in metal ion batteries.¹²⁸

Fig. 6 Theoretical storage capacity (TSC) and average open circuit voltage (OCV) of (a) Ca_xCrB₄, (b) Ca_xMoB₄, and (c) Ca_xWB₄.

3.6 Electronic structure and conductivity

A desirable anode material's high electronic conductivity is a feature that directly impacts the battery's performance. A battery's internal electronic resistance is mostly determined by its electronic conductivity. The electronic structure of the MB₄ (M = Cr, Mo, and W) monolayer was investigated using GGA-PBE calculations. Fig. S23(a–c)† reveal that the pristine monolayers are metallic in nature. Band structures show the two Dirac cones, one is located over the Fermi level and the other is located just below the Fermi level. These cones have velocity nearly equal to that of graphene. Some energy bands cross the Fermi level and show the metallic conductivity, which is the best for Ca-ion batteries. Fig. 7(a–c) represent the total density of state for one, three and six layers-adsorbed MB₄. It can be shown that when we increase the number of layers of the Ca atom, then the number of electronic states also increase at the Fermi level, which indicates the more accessible active electrons in the system. Fig. S23† represents the PDOS of pristine CrB₄, MoB₄ and WB₄, which show the main contribution of the d-state of Cr/Mo/W atom and the p-state of the B-atom and after the adsorption of full contents (6 layers) of Ca atoms; we can see from Fig. 8(d–f) that the main contribution is also due to the d-state of Cr/Mo/W atom and the p-state of the B-atom of the CrB₄, MoB₄ and WB₄ host materials. For the Ca atom, only the p-state is dominant as compared to the s-state for the CrB₄, MoB₄ and WB₄ host materials. Other states indirectly contribute to the electrical conductivity, but their influence is minimal compared to these states. It can be seen that after the adsorption of the Ca-atoms layers, the metallic nature of the materials remains the same and the electrical conductivity of the material is increased. It is observed that the charge carrier transfer to the conduction band results in an increase in the electronic conductivity, suggesting that all materials have the capacity to serve as appropriate hosts for Ca-ion batteries.

Fig. 7 Total density of states of Ca adsorption for different contents of (a) Ca_xCrB₄, (b) Ca_xMoB₄, and (c) Ca_xWB₄.

Fig. 8 PDOS of the highest contents of Ca in (a) Ca₆CrB₄, (b) Ca₆MoB₄, and (c) Ca₆WB₄.

4 Conclusions

Density functional theory calculations have been used to predict the performance of CrB₄, MoB₄ and WB₄ monolayers as anode materials for calcium ion batteries. The results shows that the electrical conductivity is enhanced, while the metallicity remains unchanged. After the adsorption of Ca atoms, the adsorption energy is steadily reduced as the quantity of adsorbed Ca ions increased. The average open circuit voltage and energy barriers are 0.45 V, 0.67 eV for CrB₄, 0.47 V and 0.72 eV for MoB₄, and 0.35 V and 0.79 eV for WB₄. For the most stable site, Ca atom transferred a charge of 1.40e to the monolayer CrB₄, 1.32e to the monolayer MoB₄ and 1.35e to the monolayer WB₄. The largest distance of the last layer to the substrate is 7.95 Å, 7.99 Å and 8.32 Å for CrB₄, MoB₄ and WB₄, respectively. ELF findings demonstrate how the covalent and ionic bonds within the MB₄ monolayer coexist, which enhances the monolayer's exceptional structural stability. The volume expansion values for CrB₄, MoB₄ and WB₄ at x = 6 are 5.94%, 6.16% and 6.31%, respectively. The calculated theoretical capacities are 3377 mA h g⁻¹, 2311 mA h g⁻¹ and 1416 mA h g⁻¹, and the energy barrier profiles show that path-1 has the lowest energy barriers of 0.67 eV, 0.72 eV and 0.79 eV for CrB₄, MoB₄ and WB₄. In conclusion, the monolayers of CrB₄, MoB₄ and WB₄ offer several advantages, including excellent stability, low diffusion barriers, and a high theoretical capacity. These materials show promise as anode materials for Ca-ion batteries and may find practical applications in future commercial battery materials. Our research aims to provide essential insights into the feasibility of incorporating monolayer MB₄ in Ca-ion battery technology.

Data availability

Data supporting the findings of this study are available in the ESI† accompanying this article. Additional data that support the findings of this study are available from the corresponding author upon reasonable request.

Author contributions

M. Kashif Masood: visualization, methodology, formal analysis, writing – original draft investigation. Jing Wang: revision, formal analysis, discussion, conceptualization, and acquisition for funding. Juntao Song: project administration, resources, visualization, supervision. Ying Liu: conceptualization, visualization, formal analysis and resources.

Conflicts of interest

Authors have no conflicts of interest to declare.

Acknowledgements

This research is funded by The National Natural Science Foundation of China (Grant No. 12174084), Science Research Project of Hebei Education Department (Grant No. ZD2021065), and The Key Program of Natural Science Foundation of Hebei Province (Grant No. A2021205024).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4ta02176b

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